#### 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.

Is there an error in this question or solution?

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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 Concept: Circles Examples and Solutions.

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