What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40, and 41?

Question: What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40, and 41?

Solution:
Here,
9² + 40² = 81 + 1600 = 1681 = 41²
∴ 9, 40, and 41 is a Pythagorean triplet. So, the triangle is right angled.

Key property about right triangles:
In a right angled triangle, the radius of the circle that circumscribes the triangle is half the hypotenuse.
In the given triangle, the hypotenuse = 41.


Therefore, the radius of the circle that circumscribes the triangle = 41/2 = 20.5 units.