M4maths Previous Puzzles

15 Nov 2013 Circle

Maximum and minimum number of intersecting points between 4 circles drawn in a plane are

OPtion

1) 16, 1
2) 18, 2
3) 10, 4
4) 12, 4
5) 20, 0
6) 10, 0
7) 22, 0
8) 12, 0
9) 16, 0
10)None of these

Solution

Every circle intersects other circle in maximum 2 points or minimum 0 point.
Total number of combinations of circle are 6 hence maximum points are 12.
Minimum intersecting points are 0.
12, 0
option 8)

Correct Option: 8 Best Solution (15)

shaswata tripathy   11 years AGO

with 2 circles, 2 points of intersections total = 2.
one more circle, 2 points of intersections,
one for each of the other 2 circles,total 3+3=6
one more circle, total 6+6= 12 points.
and minimum 0

Like? Yes (10) | No (4)  

abhi   11 years AGO

as two circle cut each other 2 cuts . third will cut 2 cut to each circle hence 4 now forth will cut it to 6 so total is 2+4+6=12
min will 0

Like? Yes (5) | No (2)  

Suman   11 years AGO

We know that in case of line segment if there are n lines in a plane the total number of intersection point is nC2.but in case of circle two circle meet in maximum two points.So n circle meet in nC2*2 points i.e 12 points......
And minimum number of intersection is always o that is well known to all....

Like? Yes (4) | No (2)  

raghuraj singh rajawat   11 years AGO

max 12 min 0

Like? Yes (2) | No   

Chandni Maurya   11 years AGO

ans=12,0
let n be the no of circles,
max no of intersecting points,
=(n-1)*2+[(n-1)*2-2]+[(n-1)*2-4]
here n=4
=>(4-1)*2+[(4-1)*2-2]+[(4-1)*2-4]
=6+4+2=12

Like? Yes (5) | No (4)  

sivaramakrishna   11 years AGO

max=4*3=12
min=0

Like? Yes (1) | No   

prakash kumar   11 years AGO

for minimum no. of intersecting points 4 circles draw in a plane with some distance intersecting point is 0.
2 circles intersect maximum points = 2
3 circles intersect maximum points = 3*2 = 6
4 circles intersect maximum points = 6*2 = 12.

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Shreesh Tripathi   11 years AGO

iu u draw 2 circle intersect at 2 point 3 at 6 point thus 4 at 12 points and minimally at 0

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himani sikarwar   11 years AGO

four circle can intersect to eachother,so maximum point of intersection is 12 and no circle can intersect in the same plain so minimum point of intersection is 0.

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R.RAVIKUMAR   11 years AGO

The mininum intersection points is 0
and max intersection points is 12
=> 2*3+2*2+2*1=12

Like? Yes (2) | No (3)  

Dr.Dipin Singh   11 years AGO

Any circle can cut other circle in max 2 points which are shared by both.
so 2 circles can intersect max at 2 (2*2*1/2)points.
3 circles can intersect max at 6 (3*2*2/2)points.
4 circles can intersect max at 12 ( 4*2*3/2) points.

Like? Yes (4) | No (5)  

Harjit kaur   11 years AGO

2nd circle intersect the 1st at 2 points
3rd ". ". ". " And 2nd at 4points
4th. ". ". ". ". ". ". And 3rd at 6 points
Thus total intersection points are2+4+6=12

Like? Yes (2) | No (3)  

Prakash kumar   11 years AGO

from picture interpretation max '12' min '0'
But what if 4 circles overlap (an intersect too)
then
max 'infinity' min '0'

Like? Yes (2) | No (3)  

gourav kumar   11 years AGO

2*3*2=12

Like? Yes (1) | No (3)  

Aditya Chittekar   11 years AGO

Each circle will intersect every circle in 2 points.
Total intersection points is 4*3= 12
Minimum will be 0

Like? Yes (1) | No (3)