# If the sides of a quadrilateral touch a circle, prove that the sum of a pair of opposite sides is equal to the sum of the other pair.

Given: sides of a quadrilateral touch a circle.

To prove: sum of a pair of opposite sides is equal to the sum of the other pair

Theorem Used: The length of two tangents drawn from an externa point are equal

Explanation:

Let ABCD is a quadrilateral which touches the circle at points P,Q,R and S. Since length of a tangent drawn from external points to a circle are equal.

DR = DS ----(i)
CR = CQ-----(ii)
AP = AS-----(iii)
BP = BQ-----(iv)

DR+CR) +AP+BP=DS+CQ+AS+BQ

DC+AB = DA+CB

Hence Proved.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Quiz | Imp. Qs. on Circle35 mins  Quiz | Imp. Qs. on Circles37 mins  Quiz | Testing Your Knowledge on Circles32 mins  Short Cut Trick to Find Area of Triangle43 mins  Quiz | Areas Related to Circles43 mins  RD Sharma | Area of Sector and Segments25 mins  Quiz | Area Related with Circles47 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 