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Byju's Answer
Standard XII
Mathematics
Combination Based on Geometry
If there are ...
Question
If there are
n
circles in a plane which gives
56
points of intersection, then the minimum value of
n
is
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Solution
The maximum number of points of intersection of
n
circles in a plane is
2
×
n
C
2
∴
2
×
n
C
2
≥
56
⇒
2
×
n
(
n
−
1
)
2
≥
56
⇒
n
2
−
n
−
56
≥
0
⇒
(
n
−
8
)
(
n
+
7
)
≥
0
⇒
n
=
8
(min)
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0
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Standard XII Mathematics
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