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 $¯ ¯¯¯¯¯¯ ¯ A B$ and $¯ ¯¯¯¯¯¯¯ ¯ C D$ are at right angles.

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Solution

Draw two circles of equal radii taking A and B as their centre such that one of them passes through the centre of the other.

Since the radii of both the circles are equal, so if one passes through the centre of the other then the later will automatically pass through the centre of the first one.

They intersect at C and D. Join AB and CD. Yes, AB and CD intersect at right angle as $∠ C O B$ is equal to $90^{\circ}$

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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 ¯¯¯¯¯¯¯¯AB and ¯¯¯¯¯¯¯¯¯CD are at right angles.

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 $¯ ¯¯¯¯¯¯ ¯ A B$ and $¯ ¯¯¯¯¯¯¯ ¯ C D$ are at right angles.