In the given figure, if quadrilateral PQRS circumscribes a circle, then PD + QB =

Question:

In the given figure, if quadrilateral PQRS circumscribes a circle, then PD + QB =

(a) PQ

(b) QR

(c) PR

(d) PS

Solution:

We know that tangents drawn to a circle from the same external point will be equal in length.

Therefore,

PD = PA …… (1)

QB = QA …… (2)

Adding equations (1) and (2), we get,

PD + QB = PA + QA

By looking at the figure we can say,

PD + QB = PQ

Therefore option (a) is the correct answer.

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