O is the center of circle to which PAX and PBY are tangents from a point P at points A and B. Q is a point on the circle, such that ∠QAX = 49° and ∠QBY = 62°. What is the measure of ∠AQB?
Show answer & explanation
Correct answer: B
Explanation
Correct Answer is option 2 i.e. 69°
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Concept |
Understanding |
Application |
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Tangent to a circle forms right angle with the radius. |
Given: ∠QAX = 49°, ∠QBY = 62° Since PAX and PBY are the tangents; ∠PAO = ∠PBO = 90°
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As shown in the figure: ∠QAO = 90 – 49 = 41° ∠QBO = 90 – 62 = 28° Since OA = OQ (radius) in triangle AOQ; ∠AQO = ∠QAO = 41° Also, OB = OQ (radius) in triangle BOQ; ∠BQO = ∠QBO = 28° Hence, ∠AQB = ∠AQO + ∠BQO = 41 + 28 = 69° |
