Quantitative Aptitude – Geometry – Circles – Let ABC be a right-angled isosceles

Quantitative Aptitude – Geometry – Triangles

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

A) 9Ï€ – 18
B) 18
C) 9Ï€
D) 9

Answer

Option (B)

Solution

As per the question from CAT 2017 – Quantitative Aptitude – Geometry – Circles,

Let AB = a (a = 6)
CQB is a semicircle of radius a/âˆš2
CPB is a quarter circle (quadrant) of radius a
So, area of semicircle = pi*a^2/4
Area of quadrant = pi*a^2/4
So, area of region enclosed by BPC, BQC = Area of tr(ABC) = 18.
Option (B)

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