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Question
PQ is a tangent to a circle with centre O at the point P. If ΔOPQ is an isosceles triangle, then ∠OQP is equal to ______.
Options
30°
45°
60°
90°
MCQ
Fill in the Blanks
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Solution
PQ is a tangent to a circle with centre O at the point P. If ΔOPQ is an isosceles triangle, then ∠OQP is equal to 45°.
Explanation:
We have OP ⊥ PQ, i.e., ∠OPQ = 90°.
ΔOPQ is isosceles
⇒ OP = PQ
⇒ ∠OQP = ∠POQ ...[∵ In a triangle, angles opposite equal sides are equal]
⇒ ∠OQP = 45°
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