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Draw different pairs of circle how many points does each pair have in common what is the maximum number of common points

Posted by Bonty Clock Gaming 2 years, 3 months ago

CBSE > Class 09 > Mathematics

1 answers

Preeti Dabral 2 years, 3 months ago

From the figure, we observe that when different pairs of circles are drawn, each pair have two points (say A and B) in common.
Maximum number of common points are two in number.

Suppose two circles C (O) and C (O’) intersect each other in three points, say A, B and C.
Then A, B and C are non-collinear points.
We know that:
There is one and only one circle passing through three non-collinear points.
Therefore, a unique circle passes through A, B and C.
$\Rightarrow$ O’ coincides with O and s = r where s and r are the radii of two circles C(O) and C(O')
A contradiction to the fact that C (O’,) $\ne$ C (O,)
$\therefore$ Our supposition is wrong.
Hence two different circles cannot intersect each other at more than two points.

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CBSE > Class 09 > Mathematics