ABC is a cyclic triangle and the bisectors of ∠BAC,

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ABC is a cyclic triangle and the bisectors of ∠BAC, ∠ABC and ∠BCA meet the circle at P, Q, and R respectively. Then the angle ∠RQP is

1. 90° - B
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2. 90° + B
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3. 90° + C
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4. 90° - A
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Correct Option: A

As per the given in question , we draw a figure of a cyclic triangle ABC and the bisectors of ∠BAC, ∠ABC and ∠BCA meet the circle at P, Q, and R

∠BQP =∠BAP

∴ ∠BQP =	∠A
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∠BQR = ∠BCR

∴ ∠BQR =	1	∠C
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∴ ∠BQP + ∠BQR =	1	(∠A + ∠C)
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⇒ ∠PQR =	1	(180° - ∠B)
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[we know that , ∠A + ∠B + ∠C = 180°]

∠PQR = 90° –	B
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