FIND THE MAXIMUM NUMBER OF POINTS OF INTERSECTION OF 8 CIRCLES.SHOW THE WORKING

though i m not sure of my method







2 circles can intersect at max 2 points of intersection







1) when a single circle intersects all the other circles







8 C 1 X 2 X 7







2) when 2 circles intersects all the other circles







8 C 2 x 2 x 6











SO ..ANS = 8 C 1 X 2 X 7 + 8 C 2 x 2 x 6 + 8 C 3 x 2 x 5 + .....







WRONG ANSWER !!!!!!!!!!!!!!

CHECK BELOW TO SEE  THE RIGHT LOGIC

Each circle can intersect another at atmost 2 points.

As we need the maximum no of points of intersection of 8 circles,

no of ways of selecting 2 circles out of 8 = 

they will intersect at   points

(This qsn is quite similar to the famous qsn " n people at a party shook hands with each other.  How many 

handshakes were there altogether?")

@ v89, that's not said, dude! Rajat Sen says that 2 circles can intersect at most at 2 points....

@v89

ofc it can...infact to get the maximum number you SHOULD take that into consideration..



Let me explain my working..



suppose there are only two circles..they can intersect atmost at only 2 points..

Now take the case of three circles..the 1st can intersect the 2nd at points, 2nd can intersect the third at 2 points, and third can intersect the 1st at two

so total no of points of intersection = 6 = 3C2 * 2



now take the case of 4 circles...

 1-->2 at 2 pts

 1-->3 at 2 pts

 1-->4 at 2 pts

 2-->3 at 2 pts

 2-->4 at 2 pts

 3-->4 at 2 pts



so total no of points of intersection = 4C2 * 2



extending this to n circles...it will be nC2 * 2

 the no of points of intersection of 2 circles is 2.