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 interior angles are of ${90}^{\circ }$.

$AD=BC$, and $AB=DC$
In rectangle, diagonals are of equal length and also these bisect each other.

$AC=BD$

$\frac{1}{2}AC=\frac{1}{2}BD$

$\therefore OA=OC=OB=OD$

so, $OA=OC=OD$, which means O point is at equal distant from A,B,C.
hence, O is equidistant from $A,B$ and $C$.