Question

ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you)

Answer 1

ABCD is a rectangle as opposite sides are equal and parallel to each other, and all the interior angles are 90º.

In a rectangle, diagonals are of equal length and also these bisect each other.

Since MBC is right-angled at B. So ∠D = 90°, AD||BC and AB||DC

ABCD is a rectangle where AB = CD and AD=BC

AC and BD are the diagonals which bisect each other.

Hence, AO = OC = BO = OD

Thus, O is equidistant from A, B, and C.