Problem K2

Geometry Level 4

Given three concentric circles, randomly select one point on each circle in such a way that, if the circle is partitioned in segments of equal length, no matter how small, there is an equal probability for the point to end up in each of the segments.

What is the probability that the center of the circles lies within the triangle?


The answer is 0.25.

Kris Hauchecorne by Kris Hauchecorne , 49, Belgium

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1 solution

Kris Hauchecorne
Dec 8, 2018

2 Helpful 0 Interesting 0 Brilliant 0 Confused

If it's the same for all possible radii of the concentric circles, we can just assume them to be very close to each other. Now the problem simply asks for the probability of formation of an acute angled triangle from any 3 points randomly selected on the circle. That probability is also 0.25, but solved in a different way.

Is this above approach valid? Please correct if I'm wrong and that it's just a coincidence that the probabilities match.

Parth Sankhe - 2 years, 6 months ago

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I believe it to be correct, but I am not a mathematician.

Kris Hauchecorne - 2 years, 6 months ago

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