Question

In the given figure, two tangents RQ, and RP and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120°, then prove that OR = PR + RQ.

Answer 1

Construction Join PO and OQ

In △POR and △QOR

OP = OQ(Radii)

RP = RQ (Tangents from the external point are congruent)

OR = OR (Common)

By SSS congruency, △POR \(\cong\) △QOR

∠PRO = ∠QRO (C.P.C.T)