चक्रीय चतुर्भुज - Revision history

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	==चक्रीय चतुर्भुज का क्षेत्रफल==		==चक्रीय चतुर्भुज का क्षेत्रफल==
	The area of a cyclic quadrilateral is <math>\sqrt{(s-a)(s-b)(s-c)(s-d)}</math> where <math>a,b,c,d</math> are the four sides of the quadrilateral and <math>s</math> is the semi perimeter which can be calculated as		चक्रीय चतुर्भुज का क्षेत्रफल <math>\sqrt{(s-a)(s-b)(s-c)(s-d)}</math> है जहाँ <math>a,b,c,d</math> चतुर्भुज की चारों भुजाएँ हैं और <math>s</math> अर्ध परिमाप है जिसे <math>s=\frac{1}{2} \times (a+b+c+d)</math> के रूप में परिकलित किया जा सकता है।

	~~<math>s=\frac{1}{2} \times (a+b+c+d)</math>. [[Area of Triangle - by Heron's formula\|Heron's formula for a triangle]] is also derived from this equation.~~

	चक्रीय चतुर्भुज का क्षेत्रफल <math>\sqrt{(s-a)(s-b)(s-c)(s-d)}</math> है जहाँ <math>a,b,c,d</math> चतुर्भुज की चारों भुजाएँ हैं और <math>s</math> अर्ध परिमाप है जिसे <math>s=\frac{1}{2} \times (a+b+c+d)</math> के रूप में परिकलित किया जा सकता है।

	त्रिभुज के लिए [[हीरोन का सूत्र]] भी इसी समीकरण से प्राप्त होता है।		त्रिभुज के लिए [[हीरोन का सूत्र]] भी इसी समीकरण से प्राप्त होता है।

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 == चक्रीय चतुर्भुज ==
-चक्रीय चतुर्भुज एक वृत्त में अंकित चार भुजाओं वाला बहुभुज होता है। इसमें दी गई भुजाओं की लंबाई के साथ अधिकतम संभव क्षेत्रफल होता है। दूसरे शब्दों में, एक वृत्त में अंकित चतुर्भुज उन भुजाओं की लंबाई के साथ अधिकतम संभव क्षेत्र को दर्शाता है।
+चक्रीय [[चतुर्भुज]] एक वृत्त में अंकित चार भुजाओं वाला बहुभुज होता है। इसमें दी गई भुजाओं की लंबाई के साथ अधिकतम संभव क्षेत्रफल होता है। दूसरे शब्दों में, एक वृत्त में अंकित चतुर्भुज उन भुजाओं की लंबाई के साथ अधिकतम संभव क्षेत्र को दर्शाता है।
 ==चक्रीय चतुर्भुज की परिभाषा ==
 चक्रीय चतुर्भुज का अर्थ है एक चतुर्भुज जो एक वृत्त में अंकित होता है। इसका मतलब है कि एक वृत्त है जो चतुर्भुज के सभी चार शीर्षों से होकर गुजरता है। शीर्षों को चक्रीय कहा जाता है। वृत्त के केंद्र को परिकेंद्र के रूप में जाना जाता है और वृत्त की त्रिज्या को परित्रिज्या के रूप में जाना जाता है।
@@ Line 8: / Line 8: @@
 नीचे दिए गए चित्र में, <math>ABCD</math> एक चक्रीय चतुर्भुज है, जिसकी भुजाओं की लंबाई <math>a,b,c,d</math> तथा विकर्ण <math>p,q</math> हैं।[[File:Cyclic quadrilateral -1.jpg|alt=Fig. 1|none|thumb|200x200px|चित्र . 1]]
 ==चक्रीय चतुर्भुज के गुणधर्म==
-The properties of a cyclic quadrilateral help us to identify this figure easily and to solve questions based on it. Some of the properties of a cyclic quadrilateral are given below:
+चक्रीय चतुर्भुज के गुण हमें इस आकृति को आसानी से पहचानने और इस पर आधारित प्रश्नों को हल करने में सहायता करते हैं। चक्रीय चतुर्भुज के कुछ गुण नीचे दिए गए हैं:
-Theorem 1:  The sum of either pair of opposite angles of a cyclic quadrilateral is <math>180^\circ</math>.
+* चक्रीय चतुर्भुज में, चतुर्भुज के सभी चार शीर्ष वृत्त की परिधि पर स्थित होते हैं।
 ==चक्रीय चतुर्भुज का क्षेत्रफल==
 The area of a cyclic quadrilateral is <math>\sqrt{(s-a)(s-b)(s-c)(s-d)}</math> where <math>a,b,c,d</math> are the four sides of the quadrilateral and <math>s</math> is the semi perimeter which can be calculated as
 <math>s=\frac{1}{2} \times (a+b+c+d)</math>. [[Area of Triangle - by Heron's formula|Heron's formula for a triangle]] is also derived from this equation.
 == उदाहरण ==
 [[File:Cyclic quadrilateral - 2.jpg|alt=Fig. 2|thumb|चित्र -2]]
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 <math>\angle BCD = 180^\circ -100^\circ =80^\circ</math>
-A cyclic quadrilateral is a four-sided polygon inscribed in a circle. It has the maximum area possible with the given side lengths. In other words, a quadrilateral inscribed in a circle depicts the maximum area possible with those side lengths.
 [[Category:वृत्त]][[Category:कक्षा-9]][[Category:गणित]]

Mani: added content

2024-11-03T06:23:18Z

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	== चक्रीय चतुर्भुज ==		== चक्रीय चतुर्भुज ==
	~~A cyclic quadrilateral is a four-sided polygon inscribed in a circle. It has the maximum area possible with the given side lengths. In other words~~, ~~a quadrilateral inscribed in a circle depicts the maximum area possible with those side lengths.~~		चक्रीय चतुर्भुज एक वृत्त में अंकित चार भुजाओं वाला बहुभुज होता है। इसमें दी गई भुजाओं की लंबाई के साथ अधिकतम संभव क्षेत्रफल होता है। दूसरे शब्दों में, एक वृत्त में अंकित चतुर्भुज उन भुजाओं की लंबाई के साथ अधिकतम संभव क्षेत्र को दर्शाता है।
	==चक्रीय चतुर्भुज की परिभाषा ==		==चक्रीय चतुर्भुज की परिभाषा ==
	A cyclic quadrilateral means a quadrilateral that is inscribed in a circle. That means there is a circle that passes through all four vertices of the quadrilateral. The vertices are said to be concyclic. The center of the circle is known as the circumcenter and the radius of the circle is known as the circumradius.		चक्रीय चतुर्भुज का अर्थ है एक चतुर्भुज जो एक वृत्त में अंकित होता है। इसका मतलब है कि एक वृत्त है जो चतुर्भुज के सभी चार शीर्षों से होकर गुजरता है। शीर्षों को चक्रीय कहा जाता है। वृत्त के केंद्र को परिकेंद्र के रूप में जाना जाता है और वृत्त की त्रिज्या को परित्रिज्या के रूप में जाना जाता है।

	~~The word~~ "~~cyclic~~" ~~is from the Greek word~~ "~~kuklos~~", ~~which means~~ "~~circle~~" or "~~wheel~~"~~. The word~~ "~~quadrilateral~~" ~~is derived from the ancient Latin word~~ "~~Quadri~~", ~~which means~~ "~~four-side~~" or "~~latus~~".		शब्द "चक्रीय" ग्रीक शब्द "कुक्लोस" से लिया गया है, जिसका अर्थ है "वृत्त" या "पहिया"। शब्द "चतुर्भुज" प्राचीन लैटिन शब्द "क्वाड्री" से लिया गया है, जिसका अर्थ है "चार भुजाएँ" या "लैटस"।

	~~In the figure given below~~, <math>ABCD</math> ~~is a cyclic quadrilateral with~~ <math>a,b,c,d</math> ~~as the side-lengths and~~ <math>p,q</math> ~~as the diagonals.~~[[File:Cyclic quadrilateral -1.jpg\|alt=Fig. 1\|none\|thumb\|200x200px\|~~Fig~~. 1]]		नीचे दिए गए चित्र में, <math>ABCD</math> एक चक्रीय चतुर्भुज है, जिसकी भुजाओं की लंबाई <math>a,b,c,d</math> तथा विकर्ण <math>p,q</math> हैं।[[File:Cyclic quadrilateral -1.jpg\|alt=Fig. 1\|none\|thumb\|200x200px\|चित्र . 1]]
	==चक्रीय चतुर्भुज के गुणधर्म==		==चक्रीय चतुर्भुज के गुणधर्म==
	The properties of a cyclic quadrilateral help us to identify this figure easily and to solve questions based on it. Some of the properties of a cyclic quadrilateral are given below:		The properties of a cyclic quadrilateral help us to identify this figure easily and to solve questions based on it. Some of the properties of a cyclic quadrilateral are given below:

Mani at 06:14, 3 November 2024

2024-11-03T06:14:23Z

@@ Line 25: / Line 25: @@
 <math>s=\frac{1}{2} \times (a+b+c+d)</math>. [[Area of Triangle - by Heron's formula|Heron's formula for a triangle]] is also derived from this equation.
-==Example ==
+== उदाहरण ==
-[[File:Cyclic quadrilateral - 2.jpg|alt=Fig. 2|thumb|Fig. 2]]1: In Fig 2, <math>ABCD</math> is a cyclic quadrilateral in which <math>AC</math> and <math>BD</math> are its diagonals.
+[[File:Cyclic quadrilateral - 2.jpg|alt=Fig. 2|thumb|चित्र -2]]
-If <math>\angle DBC =55^\circ</math>and <math>\angle BAC =45^\circ</math>, find <math>\angle BCD</math>
+यदि <math>\angle DBC =55^\circ</math>और <math>\angle BAC =45^\circ</math>हैं , <math>\angle BCD</math> ज्ञात कीजिए
-Solution:
+हल:
-<math>\angle CAD=\angle DBC =55^\circ</math>(Angles in the same segment)
+<math>\angle CAD=\angle DBC =55^\circ</math>(एक ही खंड में कोण)
-Therefore, <math>\angle DAB=\angle CAD+\angle BAC</math>
+अत:, <math>\angle DAB=\angle CAD+\angle BAC</math>
 <math>\angle DAB=55^\circ +45^\circ=100^\circ</math>
-But <math>\angle DAB+\angle BCD = 180^\circ</math>(Opposite angles of a cyclic quadrilateral)
+परंतु <math>\angle DAB+\angle BCD = 180^\circ</math>(चक्रीय चतुर्भुज के विपरीत कोण)
 <math>\angle BCD = 180^\circ -\angle DAB</math>
@@ Line 46: / Line 47: @@
 A cyclic quadrilateral is a four-sided polygon inscribed in a circle. It has the maximum area possible with the given side lengths. In other words, a quadrilateral inscribed in a circle depicts the maximum area possible with those side lengths.
@@ Line 109: / Line 61: @@
 प्रमेय 2: यदि चतुर्भुज के विपरीत कोणों के किसी युग्म का योग <math>180^\circ</math> है, तो चतुर्भुज चक्रीय होता है।
 [[Category:वृत्त]][[Category:कक्षा-9]][[Category:गणित]]

Mani: added content

2024-11-03T06:10:45Z

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← Older revision		Revision as of 11:40, 3 November 2024
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	== Cyclic Quadrilateral ==		== चक्रीय चतुर्भुज ==
			A cyclic quadrilateral is a four-sided polygon inscribed in a circle. It has the maximum area possible with the given side lengths. In other words, a quadrilateral inscribed in a circle depicts the maximum area possible with those side lengths.
			==चक्रीय चतुर्भुज की परिभाषा ==
			A cyclic quadrilateral means a quadrilateral that is inscribed in a circle. That means there is a circle that passes through all four vertices of the quadrilateral. The vertices are said to be concyclic. The center of the circle is known as the circumcenter and the radius of the circle is known as the circumradius.

			The word "cyclic" is from the Greek word "kuklos", which means "circle" or "wheel". The word "quadrilateral" is derived from the ancient Latin word "Quadri", which means "four-side" or "latus".

			In the figure given below, <math>ABCD</math> is a cyclic quadrilateral with <math>a,b,c,d</math> as the side-lengths and <math>p,q</math> as the diagonals.[[File:Cyclic quadrilateral -1.jpg\|alt=Fig. 1\|none\|thumb\|200x200px\|Fig. 1]]
			==चक्रीय चतुर्भुज के गुणधर्म==
			The properties of a cyclic quadrilateral help us to identify this figure easily and to solve questions based on it. Some of the properties of a cyclic quadrilateral are given below:
			*In a cyclic quadrilateral, all the four vertices of the quadrilateral lie on the circumference of the circle.
			* The four sides of the inscribed quadrilateral are the four chords of the circle.
			*The measure of an exterior angle at a vertex is equal to the opposite interior angle.
			*In a cyclic quadrilateral, <math>p \times q</math> = sum of product of opposite sides, where <math>p,q</math> are the diagonals.
			* The perpendicular bisectors are always concurrent.
			*The perpendicular bisectors of the four sides of the cyclic quadrilateral meet at the center O.
			*The sum of a pair of opposite angles is <math>180^\circ</math>(supplementary). Let <math>\angle A,\angle B,\angle C,\angle D</math> be the four angles of an inscribed quadrilateral. Then, <math>\angle A+\angle C =180^\circ</math> and<math>\angle B+\angle D =180^\circ</math>.
			Theorems related to Cyclic Quadrilateral are mentioned below.

			Theorem 1: The sum of either pair of opposite angles of a cyclic quadrilateral is <math>180^\circ</math>.

			Theorem 2: If the sum of a pair of opposite angles of a quadrilateral is <math>180^\circ</math>, the quadrilateral is cyclic.
			==चक्रीय चतुर्भुज का क्षेत्रफल==
			The area of a cyclic quadrilateral is <math>\sqrt{(s-a)(s-b)(s-c)(s-d)}</math> where <math>a,b,c,d</math> are the four sides of the quadrilateral and <math>s</math> is the semi perimeter which can be calculated as

			<math>s=\frac{1}{2} \times (a+b+c+d)</math>. [[Area of Triangle - by Heron's formula\|Heron's formula for a triangle]] is also derived from this equation.
			==Example ==
			[[File:Cyclic quadrilateral - 2.jpg\|alt=Fig. 2\|thumb\|Fig. 2]]1: In Fig 2, <math>ABCD</math> is a cyclic quadrilateral in which <math>AC</math> and <math>BD</math> are its diagonals.

			If <math>\angle DBC =55^\circ</math>and <math>\angle BAC =45^\circ</math>, find <math>\angle BCD</math>

			Solution:

			<math>\angle CAD=\angle DBC =55^\circ</math>(Angles in the same segment)

			Therefore, <math>\angle DAB=\angle CAD+\angle BAC</math>

			<math>\angle DAB=55^\circ +45^\circ=100^\circ</math>

			But <math>\angle DAB+\angle BCD = 180^\circ</math>(Opposite angles of a cyclic quadrilateral)

			<math>\angle BCD = 180^\circ -\angle DAB</math>

			<math>\angle BCD = 180^\circ -100^\circ =80^\circ</math>

	A cyclic quadrilateral is a four-sided polygon inscribed in a circle. It has the maximum area possible with the given side lengths. In other words, a quadrilateral inscribed in a circle depicts the maximum area possible with those side lengths.		A cyclic quadrilateral is a four-sided polygon inscribed in a circle. It has the maximum area possible with the given side lengths. In other words, a quadrilateral inscribed in a circle depicts the maximum area possible with those side lengths.

Mani at 05:46, 3 November 2024

2024-11-03T05:46:18Z

← Older revision		Revision as of 11:16, 3 November 2024
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			== Cyclic Quadrilateral ==
			A cyclic quadrilateral is a four-sided polygon inscribed in a circle. It has the maximum area possible with the given side lengths. In other words, a quadrilateral inscribed in a circle depicts the maximum area possible with those side lengths.

			== Cyclic Quadrilateral Definition ==
			A cyclic quadrilateral means a quadrilateral that is inscribed in a circle. That means there is a circle that passes through all four vertices of the quadrilateral. The vertices are said to be concyclic. The center of the circle is known as the circumcenter and the radius of the circle is known as the circumradius.

			The word "cyclic" is from the Greek word "kuklos", which means "circle" or "wheel". The word "quadrilateral" is derived from the ancient Latin word "Quadri", which means "four-side" or "latus".

			In the figure given below, <math>ABCD</math> is a cyclic quadrilateral with <math>a,b,c,d</math> as the side-lengths and <math>p,q</math> as the diagonals.
			[[File:Cyclic quadrilateral -1.jpg\|alt=Fig. 1\|none\|thumb\|200x200px\|Fig. 1]]

			== Properties of Cyclic Quadrilateral ==
			The properties of a cyclic quadrilateral help us to identify this figure easily and to solve questions based on it. Some of the properties of a cyclic quadrilateral are given below:

			* In a cyclic quadrilateral, all the four vertices of the quadrilateral lie on the circumference of the circle.
			* The four sides of the inscribed quadrilateral are the four chords of the circle.
			* The measure of an exterior angle at a vertex is equal to the opposite interior angle.
			* In a cyclic quadrilateral, <math>p \times q</math> = sum of product of opposite sides, where <math>p,q</math> are the diagonals.
			* The perpendicular bisectors are always concurrent.
			* The perpendicular bisectors of the four sides of the cyclic quadrilateral meet at the center O.
			* The sum of a pair of opposite angles is <math>180^\circ</math>(supplementary). Let <math>\angle A,\angle B,\angle C,\angle D</math> be the four angles of an inscribed quadrilateral. Then, <math>\angle A+\angle C =180^\circ</math> and<math>\angle B+\angle D =180^\circ</math>.
			Theorems related to Cyclic Quadrilateral are mentioned below.

			Theorem 1: The sum of either pair of opposite angles of a cyclic quadrilateral is <math>180^\circ</math>.

			Theorem 2: If the sum of a pair of opposite angles of a quadrilateral is <math>180^\circ</math>, the quadrilateral is cyclic.

			== Area of a Cyclic Quadrilateral ==
			The area of a cyclic quadrilateral is <math>\sqrt{(s-a)(s-b)(s-c)(s-d)}</math>
			where <math>a,b,c,d</math> are the four sides of the quadrilateral and <math>s</math> is the semi perimeter which can be calculated as

			<math>s=\frac{1}{2} \times (a+b+c+d)</math>. [[Area of Triangle - by Heron's formula\|Heron's formula for a triangle]] is also derived from this equation.

			== Example ==
			[[File:Cyclic quadrilateral - 2.jpg\|alt=Fig. 2\|thumb\|Fig. 2]]
			1: In Fig 2, <math>ABCD</math> is a cyclic quadrilateral in which <math>AC</math> and <math>BD</math> are its diagonals.

			If <math>\angle DBC =55^\circ</math>and <math>\angle BAC =45^\circ</math>, find <math>\angle BCD</math>

			Solution:

			<math>\angle CAD=\angle DBC =55^\circ</math>(Angles in the same segment)

			Therefore, <math>\angle DAB=\angle CAD+\angle BAC</math>

			<math>\angle DAB=55^\circ +45^\circ=100^\circ</math>

			But <math>\angle DAB+\angle BCD = 180^\circ</math>(Opposite angles of a cyclic quadrilateral)

			<math>\angle BCD = 180^\circ -\angle DAB</math>

			<math>\angle BCD = 180^\circ -100^\circ =80^\circ</math>



	[[File:Cyclic quadrilateral.jpg\|alt=Fig. 1\|thumb\|चित्र -1]]		[[File:Cyclic quadrilateral.jpg\|alt=Fig. 1\|thumb\|चित्र -1]]
	एक [[समांतर चतुर्भुज के गुण\|चतुर्भुज]] ABCD चक्रीय कहलाता है यदि इसके चारों शीर्ष एक वृत्त पर स्थित हों (चित्र-1 देखें)।		एक [[समांतर चतुर्भुज के गुण\|चतुर्भुज]] ABCD चक्रीय कहलाता है यदि इसके चारों शीर्ष एक वृत्त पर स्थित हों (चित्र-1 देखें)।

Mani: added internal links

2024-10-11T16:03:21Z

added internal links

← Older revision		Revision as of 21:33, 11 October 2024
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	[[File:Cyclic quadrilateral.jpg\|alt=Fig. 1\|thumb\|चित्र -1]]		[[File:Cyclic quadrilateral.jpg\|alt=Fig. 1\|thumb\|चित्र -1]]
	एक [[चतुर्भुज]] ABCD चक्रीय कहलाता है यदि इसके चारों शीर्ष एक वृत्त पर स्थित हों (चित्र-1 देखें)।		एक [[समांतर चतुर्भुज के गुण\|चतुर्भुज]] ABCD चक्रीय कहलाता है यदि इसके चारों शीर्ष एक वृत्त पर स्थित हों (चित्र-1 देखें)।

	यहाँ हमें <math>\angle A+\angle C =180^\circ</math>and <math>\angle B+\angle D =180^\circ</math>प्राप्त होता है।		यहाँ हमें <math>\angle A+\angle C =180^\circ</math>and <math>\angle B+\angle D =180^\circ</math>प्राप्त होता है।

Ramamurthy at 15:05, 10 October 2024

2024-10-10T15:05:18Z

← Older revision		Revision as of 20:35, 10 October 2024
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	[[File:Cyclic quadrilateral.jpg\|alt=Fig. 1\|thumb\|चित्र -1]]		[[File:Cyclic quadrilateral.jpg\|alt=Fig. 1\|thumb\|चित्र -1]]
	एक चतुर्भुज ABCD चक्रीय कहलाता है यदि इसके चारों शीर्ष एक वृत्त पर स्थित हों (चित्र-1 देखें)।		एक [[चतुर्भुज]] ABCD चक्रीय कहलाता है यदि इसके चारों शीर्ष एक वृत्त पर स्थित हों (चित्र-1 देखें)।

	यहाँ हमें <math>\angle A+\angle C =180^\circ</math>and <math>\angle B+\angle D =180^\circ</math>प्राप्त होता है।		यहाँ हमें <math>\angle A+\angle C =180^\circ</math>and <math>\angle B+\angle D =180^\circ</math>प्राप्त होता है।

Mani: added content

2024-09-11T02:12:44Z

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← Older revision		Revision as of 07:42, 11 September 2024
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	== उदाहरण ==		== उदाहरण ==
	[[File:Cyclic quadrilateral - 2.jpg\|alt=Fig. 2\|thumb\|चित्र -2]]		[[File:Cyclic quadrilateral - 2.jpg\|alt=Fig. 2\|thumb\|चित्र -2]]
	1: ~~In Fig~~ 2, <math>ABCD</math> ~~is a cyclic quadrilateral in which~~ <math>AC</math> ~~and~~ <math>BD</math> ~~are its diagonals.~~		1: चित्र 2 में, <math>ABCD</math> एक चक्रीय चतुर्भुज है जिसमें <math>AC</math> और <math>BD</math> इसके विकर्ण हैं।

	If <math>\angle DBC =55^\circ</math>~~and~~ <math>\angle BAC =45^\circ</math>, ~~find~~ <math>\angle BCD</math>		यदि <math>\angle DBC =55^\circ</math>और <math>\angle BAC =45^\circ</math>हैं , <math>\angle BCD</math> ज्ञात कीजिए

	~~Solution~~:		हल:

	<math>\angle CAD=\angle DBC =55^\circ</math>(~~Angles in the same segment~~)		<math>\angle CAD=\angle DBC =55^\circ</math>(एक ही खंड में कोण)

	~~Therefore~~, <math>\angle DAB=\angle CAD+\angle BAC</math>		अत:, <math>\angle DAB=\angle CAD+\angle BAC</math>

	<math>\angle DAB=55^\circ +45^\circ=100^\circ</math>		<math>\angle DAB=55^\circ +45^\circ=100^\circ</math>

	~~But~~ <math>\angle DAB+\angle BCD = 180^\circ</math>(~~Opposite angles of a cyclic quadrilateral~~)		परंतु <math>\angle DAB+\angle BCD = 180^\circ</math>(चक्रीय चतुर्भुज के विपरीत कोण)

	<math>\angle BCD = 180^\circ -\angle DAB</math>		<math>\angle BCD = 180^\circ -\angle DAB</math>

Mani: added content

2024-09-11T02:07:31Z

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← Older revision		Revision as of 07:37, 11 September 2024
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	[[File:Cyclic quadrilateral.jpg\|alt=Fig. 1\|thumb\|चित्र -1]]		[[File:Cyclic quadrilateral.jpg\|alt=Fig. 1\|thumb\|चित्र -1]]
	~~A quadrilateral~~ ABCD ~~is called cyclic if all the four vertices~~		एक चतुर्भुज ABCD चक्रीय कहलाता है यदि इसके चारों शीर्ष एक वृत्त पर स्थित हों (चित्र-1 देखें)।

	~~of it lie on a circle (see Fig 1).~~		यहाँ हमें <math>\angle A+\angle C =180^\circ</math>and <math>\angle B+\angle D =180^\circ</math>प्राप्त होता है।

	~~Here we find that <math>\angle A+\angle C =180^\circ</math>and <math>\angle B+\angle D =180^\circ</math>.~~		चक्रीय चतुर्भुज से संबंधित प्रमेय नीचे उल्लिखित हैं।

	~~Theorems related to Cyclic Quadrilateral are mentioned below.~~		प्रमेय 1: चक्रीय चतुर्भुज के विपरीत कोणों के किसी भी युग्म का योग <math>180^\circ</math> होता है।

	~~Theorem 1: The sum of either pair of opposite angles of a cyclic quadrilateral~~		प्रमेय 2: यदि चतुर्भुज के विपरीत कोणों के किसी युग्म का योग <math>180^\circ</math> है, तो चतुर्भुज चक्रीय होता है।

	~~is <math>180^\circ</math>.~~

	~~Theorem~~ 2: ~~If the sum of a pair of opposite angles of a quadrilateral is~~ <math>180^\circ</math>,

	~~the quadrilateral is cyclic.~~

	== उदाहरण ==		== उदाहरण ==