SarkariPYQ

SSC CGL 2021 PYQ — Question 65

SSC CGL - 17 Aug 2021 - Shift 1 • Quantitative Aptitude • Q65

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In a circle with centre O, PAX and PBY are the tangents of the circle at points A and B, from an external point P. Q is any point on the cirlce such that ∠QAX = 59° and ∠QBY = 72°. What is the measure of ∠AQB?

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Correct answer: C

Explanation

The correct answer is Option 3 i.e 49°.

From the given figure one can conclude that,

OA = OB = OQ = Radius.

∠OAX=∠OBY=90°\angle OAX = \angle OBY = 90°

Now ∠\angleOAQ = 90° - 59° = 31°.

∠\angleOBY = 90° - 72° = 18°.

Here OA = OQ so ∠\angleOAQ = ∠\angleOQA = 31°.

OB = OQ so ∠\angleOBQ = ∠\angleOQB = 18°

∠\angleAQB =   ∠\angleOQA +  ∠\angleOQB = 31 + 18 = 49°.