No products in the cart.

Prove that opposite side of a …

CBSE, JEE, NEET, CUET

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Prove that opposite side of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Posted by Pihu ✨ 4 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 4 years, 3 months ago

Let ABCD be a quadrilateral circumscribing a circle with centre O.
Now join AO, BO, CO, DO.
From the figure, ∠DAO=∠BAO [Since, AB and AD are tangents]
Let ∠DAO=∠BAO=1
Also ∠ABO=∠CBO [Since, BA and BC are tangents]
Let ∠ABO=∠CBO=2
Similarly we take the same way for vertices C and D
Sum of the angles at the centre is 360^o
Recall that sum of the angles in quadrilateral, ABCD = 360^o

= 2(1+2+3+4)=360^o
=1+2+3+4=180^o
In ΔAOB, ∠BOA=180−(1+2)
In ΔCOD, ∠COD=180−(3+4)
∠BOA+∠COD=360−(1+2+3+4)

=360^o–180^o
=180^o

Since AB and CD subtend supplementary angles at O.
Thus, opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

ANSWER

http://mycbseguide.com/examin8/

Related Questions

sin60° cos 30°+ cos60° sin 30°

Posted by Vanshika Bhatnagar 1 year, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Prove that root 8 is an irration number

Posted by Sahil Sahil 1 year, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

Few rules to keep homework help section safe, clean and informative.

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

Posted by Hari Anand 3 months ago

CBSE > Class 10 > Mathematics

0 answers

Find the nature of quadratic equation x^2 +x -5 =0

Posted by Parinith Gowda Ms 1 week, 2 days ago

CBSE > Class 10 > Mathematics

0 answers

Venu Gopal has twice

Posted by Lakshay Kumar 9 months, 3 weeks ago

CBSE > Class 10 > Mathematics

0 answers

If 1/2 is a root of equation x^2+kx- 5/4 =0 , then what is the value of k

Posted by Parinith Gowda Ms 1 week, 2 days ago

CBSE > Class 10 > Mathematics

1 answers

This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

Few rules to keep homework help section safe, clean and informative.

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

Posted by Kanika . 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Is it possible to design a rectangular mango Grove whose length is twice it's breadth, and the area is 800m²? If so, find it's length and breadth

Posted by Akshata Choukse 1 year, 1 month ago

CBSE > Class 10 > Mathematics

0 answers

(A + B )²

Posted by Abhishek Gupta 1 year, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

X-y=5

Posted by Kishan Thakur 11 months, 1 week ago

CBSE > Class 10 > Mathematics

1 answers

myCBSEguide App

myCBSEguide

Trusted by 1 Crore+ Students

Test Generator

Test Generator

Create papers online. It's FREE.

CUET Mock Tests

CUET Mock Tests

75,000+ questions to practice only on myCBSEguide app

Google Play

Download myCBSEguide App