Question

A circle is inscribed in quadrilateral PQRS prove that : QR +SP=QP+SR​

Answer 1

Step-by-step explanation:

Answer is in the photo. Hope it will be helpful to u

Answer 2

Given:

A circle is inscribed in quadrilateral PQRS

To prove:

QR +SP=QP+SR

Solution:

1) According to the question in PQRS a circle is touched the quadrilateral at the points P, Q, R, S.

2) As per the rule of the tangent of the circle that the tangents of the circle from a point are equal to each other.

RA=RB

SA=SD

PC=PD

CQ=QB

3) Add all these equations above mentioned

RA+SA+PC+CQ = RB+SD+PD+QB

SR+PQ=SP+RQ (RA+SA = SR, PC+CQ=PQ, RB+QB=RQ, SD+PD=SP)

Hence proved.