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