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SSC CHSL 2020 PYQ — Question 71

SSC CHSL - 19th October 2020 - Shift 1 • Quantitative Aptitude • Q71

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A pair of tangents AB and AC are drawn from a point which is at a distance of 10 cm from the centre O of a circle of radius 6 cm, then the area in cm2 of quadrilateral ABOC, is:

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Correct answer: B

Explanation

The correct answer is Option 2 i.e. 48.

Understanding/Application

Since △ABO is congruent to △ACO, the area of ABOC is twice the area of △ABO.
In △ABO, OA=10cm, OB=6cm.
Since tangent is perpendicular to the radius at the point of contact, by Pythagoras' theorem, we have -

AB2 = OA2 - OB2 = 100 - 36

AB = 8 cm 

Area of  △ABO = 1/2 × AB × OB = 1/2 × 8 × 6 = 24 cm2

The area of ABOC = 2 × 24 = 48 cm2