there are 4, 5 and 6 points on the three parallel and co-planar lines .if no set of four or more points is cyclic and no set of three points lying on distinct lines is collinear then the number of circles passing through exactly three points is??

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there are 4, 5 and 6 points on the three parallel and co-planar lines .if no set of four or more points is cyclic and no set of three points lying on distinct lines is collinear then the number of circles passing through exactly three points is??

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saideep 16th Mar, 2021

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Ayush 17th Mar, 2021

Hello candidate,

In the Question it's mentioned that no more than 4 points can lie on the circle of the circle cannot pass through more than a set of four points.

So, it's obvious that from the parallel lines only one point can be included. Hence, here are the following combinations which can be found-

Case I: 4C1* 5C1*6C2

Case II: 4C1* 5C2*6C1

Case III: 5C2* 6C2

Case IV: 5C3* 6C1

Case V: 6C3* 5C1

Hope that This answer was helpful!!

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