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

Draw lines $AD$ and $DC$ such that $AD||BC$, $AB||DC$
$AD = BC$, $AB = DC$
$ABCD$ is a rectangle as opposite sides are equal and parallel to each other and all the interior angles are of $90\degree$.
In a rectangle, diagonals are of equal length and also these bisect each other.
Hence, $AO = OC$ = $BO = OD$

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