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. \(9\pi-18\)
• B. 18
• C. \(9\pi\)
• D. 9

Answer 1

The Correct Option is B

Let AB=a (where a=6).
CQB is a semicircle with a radius \(\frac{a}{\sqrt{2}}\)
CPB is a quarter circle (quadrant) with a radius of a. 
Therefore, the area of the semicircle is \(\frac{\pi a^2}{4}\)
Area of quadrant \(=\frac{\pi a^2}{4}\)
Therefore, the area of the region enclosed by BPC, BQC is equal to the area of triangle ABC, which is 18.