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There are five points A,B,C,D and E. no ...

There are five points A,B,C,D and E. no three points are collinear and no four are concyclic. If the line AB intersects of the circles drawn through the five points. The number of points of intersection on the line apart from A and B is

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The correct Answer is:
8
Number of circles through ACD, ACE, ADE intersect the line AB=3 and
Number of circles through BCD, BCE, BDE intersect the line AB=3 and
Number of circles through CDE intersects the line AB=2 hence, number of points of intersection=3+3+2=8.
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