ABC is a right angled triangle. O is the mid point of hypotenuse AC, such that OA = OC

Draw CD||AB and join AD, such that AB = CD and AD = BC

Now quad ABCD is a rectangle, since each angle is a right angle and opposite sides are equal and

parallel.

We know in a rectangle diagonals are of equal length and they bisect each other.

Therefore, AC = BD

And also, AO = OC =BO =OD

Hence, O is equidistance from A, B and C.