A geometry problem by Mehul Chaturvedi

Geometry Level 3

What is the maximum number of regions (in a circle) that can be created by drawing 3 chords in a circle?


The answer is 7.

Mehul Chaturvedi by Mehul Chaturvedi , 22, India

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3 solutions

Abhigyan Shekhar
Oct 16, 2014

This can be solved with a general formula- n(n+1)/2+1 So, by solving we get, 3(4)/2+1=7

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Aniruddha Bagchi
Jan 18, 2017

This problem is similar to the concept of Lazy Caterer's Sequence. Check out this link for further details : (https://en.m.wikipedia.org/wiki/Lazy caterer's sequence)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

If the three lines intersect at a point, SIX sectors are produced. However if one is shifted, another triangle is produced with vertices at the three points of intersections. So now it is SEVEN . What ever we do, the points of intersection can not be increased to be more than three. So 7
is the maximum.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I believe the answer is 6, not 7. because if I look up the definition of sector, I always see it defined as a part of the circle "formed by 2 radii and an arc". Hence the lines producing the sectors must all go through the center (to produce radii).

Victor Pol - 4 years, 5 months ago

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