What is the area of ​​the circumcircle of a right triangle?

When the hypotenuse (H) of a right triangle is given, use the formula πH²/4 to find the area of ​​the circumcircle of the right triangle.

This formula is derived by exploiting the fact that the circumscribed circle touches all the angles of the triangle, in this case the hypothetical maximum length between two points passing through the center of the circle. This makes the hypotenuse the diameter of the circle.

This is why the area of ​​a circle is πd²/4. (d = 2r) Replace d with H.

Example

Hypotenuse = 8

Circle area = 50.26

Example code

Live demo

#include <stdio.h>
int main(void) {
   int H = 14;
   float pie = 3.14;
   float area = (float)((pie*H*H)/4);
   printf("the area of circumcircle of a right angled triangle of Hypotenuse %d is %f",H,area);
   return 0;
}

Output

the area of circumcircle of a right angled triangle of Hypotenuse 14 is 153.860016

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