2018 · Q91
In the figure given below, {ABC} is a right-angled triangle where A=90^{}, AB=p{ cm} and AC=q{ cm}. On the three sides as diameters semicircles are drawn as shown in the figure. The area of the shaded portion, in square {cm}, is
Elementary MathematicsCircles
- Apqpq
- Bπ(p2+q2)2/{\pi(p^2+q^2)}{2}
- Cπ(p2+q2)\pi(p^2+q^2)
- Dpq2/{pq}{2}
Explanation
The sum of the semicircles on the two legs exactly equals the semicircle on the hypotenuse (since p^2 + q^2 = hypotenuse^2). The shaded area therefore equals the area of the right triangle itself: pq/2. Hence option D.