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प्रश्न
In the given figure, PT is tangent to a circle with centre O. Chord PQ subtends an angle of 65° at the centre. The measure of ∠QPT is ______.
पर्याय
65°
57.5°
67.5°
32.5°
MCQ
रिकाम्या जागा भरा
उत्तर
In the given figure, PT is tangent to a circle with centre O. Chord PQ subtends an angle of 65° at the centre. The measure of ∠QPT is 32.5°.
Explanation:
∠OPQ + ∠OQP + ∠QOP = 180°
2∠OPQ + 65° = 180°
∠OPQ = `(180 - 65)/2`
= 57.5°
∠OPT = 90°
∠OPQ + ∠QPT = 90°
∠QPT = 90° − 57.5°
= 32.5°
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