Question

In Fig. 10.86, if quadrilateral PQRS circumscribes a circle, then PD + QB =
A. PQ
B. QR
C. PR
D. PS

Answer 1

In Fig. 10.86, if quadrilateral PQRS circumscribes a circle, then PD + QB = PQ

Option A is correct.

The lengths of two tangents drawn from an external point to a circle are equal.

Therefore,

From the figure, we have,

PD = PA …… (1)

QB = QA …… (2)

On adding equations (1) and (2), we get

PD + QB = PA + AQ

From the above figure, we have PA + AQ = PQ

Hence, we get

PD + QB = PQ

Therefore, the measure of PD + QB is equal to the measure of PQ.