Question

In the following figure, PQ and PR are tangents to the circle, with centre O. If ∠ QPR = 60° , calculate:

∠ OQR 

Answer 1

Join QR.

In Δ QOR,

OQ = QR (Radii of the same circle)

∴ ∠ OQR = ∠ QRO  .....(i)

but , ∠OQR + ∠QRO + ∠QOR = 180°

∠OQR + ∠ QRO +120° = 180°

∠OQR + ∠QRO = 60°

from (i)

2 ∠OQR = 60°

∠ OQR = 30°