Question

PQRS is a quadrilateral. Prove that PQ + QS + RS + RP > PS+ QR.





please give correct answer​

Answer 1

Step-by-step explanation:

Given:

Quadrilateral PQRS circumscribes a circle

To prove that:

PQ+RS=PS+QR

Proof:

Lengths of tangents drawn to a circle from an external point are equal.

Hence, PA=PD(i)

QA=QB(ii)

RB=RCiii)

SC=SD(iv)

LHS

PQ+RS=PA+AQ+RC+CS(v)

RHS

PS+QR=PD+DS+QB+BRvi)

=PA+CS+AQ+RC using equations (i), (ii), (iii) and (iv)

From above, it can be seen LHS = RHS

Hence proved