Question

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("AB")` and `overline"CD"` are at right angles.

Answer 1

Let us draw two circles of same radius which are passing through the centres of the other circle.

Here, point A and B are the centres of these circles and these circles are intersecting each other at point C and D.

In quadrilateral ADBC,

AD = AC (Radius of circle centered at A)

BC = BD (Radius of circle centered at B)

As radius of both circles are equal, therefore, AD = AC = BC = BD

Hence, `square"ADBC"` is a rhombus and in a rhombus, the diagonals bisect each other at 90°. Hence, `overline("AB")` and `overline"CD"` are at right angles.