# Ex.3.4 Q6 Understanding Quadrilaterals Solution - NCERT Maths Class 8

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## Question

$$ABC$$ is a right-angled triangle and $$O$$ is the midpoint 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).

Video Solution
Ex 3.4 | Question 6

## Text Solution

What is Known?

$$ABC$$ is a right-angled triangle and $$O$$ is the midpoint of the side opposite to the right angle.

What is Unknown?

Why $$O$$ is equidistant from $$A, B$$ and $$C$$

Reasoning:

Since, two right triangles make a rectangle and in any rectangle, diagonals bisect each other.

Steps:

$$ABCD$$ is a rectangle as opposite sides are equal and parallel to each other and all the interior angles are of $$90^\circ .$$

\begin{align}{\rm{AD}}\left| {\left| {{\rm{BC}},{\rm{AB}}} \right|} \right|{\rm{DC}}\\{\rm{AD }} = {\rm{BC}},{\rm{ AB }} = {\rm{ DC}}\end{align}

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

Hence, $${\rm{AO }} = {\rm{ OC }} = {\rm{ BO }} = {\rm{ OD}}$$

Since, two right triangles make a rectangle where $$O$$ is equidistant point from $$A, B, C$$ and $$D$$ because $$O$$ is the mid-point of the two diagonals of a rectangle.

So, $$O$$ is equidistant from $$A, B, C$$ and $$D.$$

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