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The number of different circles passing ...

The number of different circles passing through the points A,B,C,D,E,F and G as shown in the adjacent figure.

Text Solution

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We know that from three non-collinear points one and only one circle can be drawn.
Hence, the number of different circles.
=Number of 3 non-collinear points selected from the given figure
`=""^(5)C_(2)xx""^(2)C_(1)+""^(4)C_(1)xx""^(2)C_(2)`
`=20+4=24`
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