A rectangular triangle with 12cm and 16cm legs is inscribed in a circle.

A rectangular triangle with 12cm and 16cm legs is inscribed in a circle. Find the length of the median drawn to the hypotenuse.

Given a right-angled triangle with legs 12cm and 16cm inscribed in a circle. Find the length of the median drawn to the hypotenuse. We know if a right-angled triangle is inscribed in a circle, then the hypotenuse is the diameter of the circle and the median drawn to the hypotenuse is equal to the radius of the circle.

In order to find the median, we need to calculate the hypotenuse. Find the hypotenuse using the Pythagorean theorem

c ^ 2 = 12 ^ 2 + 16 ^ 2 = 144 + 256 = 400;

c = 20 cm.

Now, let’s find the length of the median drawn to the hypotenuse

m = c / 2 = 20/2 = 10 cm.

Answer: 10 cm.