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

Answer 1

Produce BO to D such that $BO=OD$. Join AD and DC. Then ABCD is a rectangle. In the rectangle ABCD, its diagonals AC and BD are equal and bisect each other at O,
$\therefore OA=OC$ and $OB=OD$
But $AC=BD$
Therefore, $OA=OB=OC$
Thus, O is equidistant from $A,BandC.$