Triangle abc is right angled at c. m is the mid point of ab. prove that cm = 1/2 of ab

we know that any triangle which is inscribed in a semicircle is a right angle triangle.

let a and b be the ends of the diameter and c be the point on the periphery.

so according to question m is the center of the circle

so we have cm = R (radius of the circle)

and ab= 2R

clearly cm = 1/2 ab