### Semi-circle covering n points : Puzzle

**Problem :**(Posed by Saurabh Joshi, IIT Kanpur in his blog)

Given n points drawn randomly on the circumference of a circle, what is the probability they will all be within any common semicircle?

**Solution :**

Highlight the part between the * symbols for the answer.

*

If a semi-circle covering all n points, indeed exists, then, a semi-circle covering all n points and starting from one of the points in a clock-wise direction also exists.

:)

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