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n Fig. 2, PQ and PR are two tangents to a circle with centre O. If ∠QPR = 46°, then ∠QOR equals - CBSE Class 10 - Mathematics

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Question

n Fig. 2, PQ and PR are two tangents to a circle with centre O. If ∠QPR = 46°, then ∠QOR equals:

(A) 67°
(B) 134°
(C) 44°
(D) 46°

Solution

Given: ∠QPR = 46°
PQ and PR are tangents.
Therefore, the radius drawn to these tangents will be perpendicular to the tangents.
So, we have OQ ⊥ PQ and OR ⊥ RP.
⇒ ∠OQP = ∠ORP = 90
So, in quadrilateral PQOR, we have
∠OQP +∠QPR + ∠PRO + ∠ROQ = 360
⇒ 90° + 46° + 90° + ∠ROQ = 360
⇒ ∠ROQ = 360 − 226 = 134

Hence, the correct option is B.

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Solution n Fig. 2, PQ and PR are two tangents to a circle with centre O. If ∠QPR = 46°, then ∠QOR equals Concept: Circles Examples and Solutions.
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