UPSC CDS 2 2021 Math Paper

Given,
Radius of circumcircle of right angled triangle =10cmIn the right angled triangle, the hypotenuse is the diameter of the circumcircle and its centre is the mid-point of the hypotenuse.
i.e., OA=OC=10cm
∴ Hypotenuse
=AC=2×(10)=20cm
The altitude drawn to the hypotenuse
=BO=8cm
∴ Area of the right angled triangle
‌‌=‌

1

2

×AC×BO
‌‌=‌

1

2

×20×8=80cm2
Hence, area of the triangle is 80cm2.