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SSC CGL 2021 PYQ — Question 56

SSC CGL - 18 Aug 2021 - Shift 1 • Quantitative Aptitude • Q56

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AB is a chord of a circle in minor segment with centre O. C is a point on the minor arc of the circle between the points A and B. The tangents to the circle at A and B meet at the point P. If ∠ACB = 102º, then what is the measure of ∠APB?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 24º

∠\angleACB  + ∠\angleADC = 180 (Cyclic quadrilateral)

∠\angleADC = 180 - 102 = 78°

∠\angleAOB = 2 × ∠\angleADC ( Angle subtended by the arc at the centre is twice of the angle subtended by the same arc at the circumference)

∠\angleAOB = 2 × 78 = 156°.

∠\angleAOB + ∠\angleAPB = 180°

  ∠\angleAPB = 180 - 156 = 24°.