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Question

In the given figure, O is centre of the circle. Circle has 3 tangents. If ∠ QPR = 45 0 , then what is the value (in degrees) of ∠ QOR ?

A 67.5 Correct Answer Incorrect Answer
B 72 Correct Answer Incorrect Answer
C 78.5 Correct Answer Incorrect Answer
D 65 Correct Answer Incorrect Answer

Solution

We draw line OL and OM which will be Ʇ (by tangent)   We draw another line OP which bisect angle P ON will be at 900 by tangent prop Angle ∠ L = ∠ N = 900 ∆ OLQ and ∆ OQN are similar (OQ common) ∠ OQL and ∠ OQN will be equal ∠ Q = 67.50 ∠ OQL =∠ OQN = 112.5/2 = 56.250 ∠ QON = 33.750 , same for ∠ RON= 33.750 ∠ QOR = 67.5

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