In the given figure, O is the center of the circle. Circle has 3 tangents. If ∠QPR = 45°, then what is the value (in degrees) of ∠QOR?
Explanation:
In ΔPRQ
∠Q + ∠R + ∠P = 180°
⇒ 180 – 2x + 180 – 2y + 45 = 180
⇒ x + y = 225/2 = 112.5
In ΔQOR
∠OQR + x + y = 180°
⇒ ∠OQR = 180 – (x + y) = 180 – 112.5 = 67.5°
Hence, option (a).
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