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 and are at right angles.

The answer is

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, is a rhombus and in a rhombus, the diagonals bisect each other at 90°. Hence, and are at right angles.

But I think they form perpendicular bisectors and not right angle . So what would be the correct answer ?

Dear Student,

If the diagonals are perpendicular bisector then it means that both are inclined at an angles of 90° (which is a right angle) and also bisect each other i.e., if AB and CD intersect at O  then AO = OB and OC = OD.

Hope you get it!!

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