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.
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2
Answer:
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 O.
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, ADBC is a rhombus and i an rhombus, the diagonals bisect each other at 90
o
.
Hence,
AB
and
CD
are at right angles.
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