Archit's Challenge 5
Geometry
Level
5
Let be a 16 sided regular polygon inscribed in a circle. Find the number of ways of selecting three points such that when they are joined they form an obtuse angled triangle.
The answer is 336.
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1 solution
we select a point anywhere on the circle there would be a point diametrically opposite to it and 7 points on two semicircles created by diameter and we know angle subtended by a chord minor segment created is obtuse. summing it up for all the cases after removing repeated cases we get 336.