CAT 2017 Geometry & Mensuration Question (Hard)

Question

Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq. cm, of the region enclosed by BPC and BQC is

Accepted Answer

Step 1 Area of semicircle BQC Radius So, area of semicircle _ 2 pi r 2 2 pi 3 2 2 pi 18 9 pi --- Step 2 Area of sector BPC arc centered at A Angle since triangle is right-angled at A Radius AB 6 So area of sector of _ 360 cdot pi r 2 4 cdot pi cdot 6 2 4 cdot pi cdot 36 9 pi But this is the full sec

CAT 2017

Quantitative

Geometry & Mensuration

Hard

Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq. cm, of the region enclosed by BPC and BQC is :

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