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 $C.$

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Solution

## Explaining why $O$is equidistant from $A,B$ and $C$:Construction: Draw two lines $AD$ and $DC$ such that $\mathrm{AD}\mathrm{II}\mathrm{BC}$ and $\mathrm{AB}\mathrm{II}\mathrm{DC}$$\mathrm{AD}=\mathrm{BC},\mathrm{AB}=\mathrm{DC}$Since, $\square \mathrm{ABCD}$ is a rectangle.Opposite sides are parallel and equal to each other and all the interior angles are right angles.The property of rectangle states that the diagonals are of equal length and bisect each other.Hence, $\mathrm{AO}=\mathrm{OC}=\mathrm{BO}=\mathrm{OD}.$Therefore , $O$ is equidistant from $A,B$ and $C.$

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