The lines L_1, L_2, ldots, L_{20} are distinc | vedclass

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(B) There are $20$ lines in total. Let $S_1 = \{L_1, L_3, \ldots, L_{19}\}$ be the set of $10$ parallel lines and $S_2 = \{L_2, L_4, \ldots, L_{20}\}$

Vedclass · Accepted Answer

$101$

Vedclass · Answer

(B) There are $20$ lines in total. Let $S_1 = \{L_1, L_3, \ldots, L_{19}\}$ be the set of $10$ parallel lines and $S_2 = \{L_2, L_4, \ldots, L_{20}\}$ be the set of $10$ lines passing through a common point $P$.The total number of pairs of lines is given by $\binom{20}{2} = \frac{20 	imes 19}{2} = 190$.Since the $10$ lines in $S_1$ are parallel,they do not intersect. Thus,we lose $\binom{10}{2} = 45$ intersection points.Since the $10$ lines in $S_2$ are concurrent at point $P$,they intersect at only one point instead of $\binom{10}{2} = 45$ distinct points. Thus,we lose $45 - 1 = 44$ intersection points.The maximum number of intersection points is $190 - 45 - 44 = 101$.

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