Q. 19

Mark the correct alternative in the following:

Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given point is

A. 216

B. 156

C. 172

D. none of these

Answer :

We need at least three points to draw a circle that passes through them.


Now, number of circles formed out of 11 points by taking three points at a time = 11C3


= 165


Number of circles formed out of 5 points by taking three points at a time = 5C3


= 10


It is given that 5 points lie on once circle.


Required number of circles =


165 – 10 + 1


= 156

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