3 Points Make a Circle

Geometry Level 2

I randomly choose 3 points in space. What is the probability that these three points are on the perimeter of some circle? (Assume that the 3 points are not colinear, or on the same line)


The answer is 1.000.

Joshua Lowrance by Joshua Lowrance , 18, USA

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1 solution

Parth Sankhe
Jan 24, 2019

Any three non collinear points will always be on some circle, because the points will form a triangle, and every triangle has a circumcircle, a circle touching all three vertices of the triangle.

0 Helpful 0 Interesting 2 Brilliant 0 Confused

following my failure to understand that probability is answered as a real number between 0 and 1, i suppose the question should be slightly clearer on the format of answer, as i typed in 100 (as in 100%) which was wrong

Goh Choon Aik - 2 years, 4 months ago

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