# Let A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at $C$ and $D$. Examine whether $\overline{\mathrm{AB}}$ and $\overline{\mathrm{CD}}$ are at right angles.

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Given:

$A, B$ are the centres of two circles of equal radii.

To do:

We have to examine whether $\overline{AB}$ and $\overline{CD}$ are at right angles.

Solution:

Let us draw two circles of equal radii so that each one of them passes through the center of the other.

Mark the centres of these circles as $A$ and $B$ respectively.

The circles intersect each other at $C$ and $D$ respectively.

Join $AC, BC, BD, AD$

Therefore,

A quadrilateral $ADBC$ is formed.

From the quadrilateral $ADBC$,

$AD = AC = BC = BD$  (Radius of both the circles is equal)

Hence, the quadrilateral formed is a rhombus.

We know that,

A rhombus has all the sides equal and its diagonals bisect each other at $90^o$.

Hence, $\overline{AB}$ and $\overline{CD}$ are at right angles.

Updated on 10-Oct-2022 13:37:27