The greatest possible number of points of int | vedclass

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(D) To find the maximum number of intersection points,we consider the following interactions:$1$. Intersection between $8$ straight lines: The maximum

Vedclass · Accepted Answer

$104$

Vedclass · Answer

(D) To find the maximum number of intersection points,we consider the following interactions:$1$. Intersection between $8$ straight lines: The maximum number of points is given by $^8C_2 = \frac{8 	imes 7}{2} = 28$.$2$. Intersection between $4$ circles: Each pair of circles can intersect at $2$ points. The maximum number of points is $^4C_2 	imes 2 = 6 	imes 2 = 12$.$3$. Intersection between $8$ straight lines and $4$ circles: Each line can intersect each circle at $2$ points. The maximum number of points is $^8C_1 	imes ^4C_1 	imes 2 = 8 	imes 4 	imes 2 = 64$.Total points $= 28 + 12 + 64 = 104$.

The greatest possible number of points of intersection of $8$ straight lines and $4$ circles is

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