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 isA. 216B. 156C. 172D. none of these

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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