Q. 44.0( 4 Votes )

Let us prove that for a quadrilateral circumscribed about a circle, the angles subtended by any two opposite sides at the centre are supplementary to each other.

Answer :


Let us assume OAD = OAB = a

OBC = OBA = b

OCD = OCB = c

ODC = ODA = d

Since ABCD is a quadrilateral, so

2 (a + b + c + d) = 3600

a + b + c + d = 1800 …Equation (i)


AOB = 1800- (a + b)


COD = 1800-(c + d)

AOB + COD = 3600–(a + b + c + d)

Putting the value from Equation (i) we get

AOB + COD = 3600–1800

AOB + COD = 1800

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Area Related with the Circle45 mins
Quiz | Area Related with Circles47 mins
Quiz | A Letter to God39 mins
A Letter to God45 mins
A Letter to God50 mins
How to build a strong Vocabulary?53 mins
Time-Management: A key to Success37 mins
Let's Calculate - A Guide to an Economist's Dictionary54 mins
Tricks to MemoriseFREE Class
Smart and Effective study is the Key of success45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses