perplexus.info :: Probability : Triangular Polygons

Triangular Polygons (Posted on 2011-08-12)

Three points have been chosen randomly from the vertices of a n-sided regular polygon.

Determine the probability (in terms of n) that they form (a) an acute triangle; (b) a right triangle?

Submitted by K Sengupta

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Solution: (Hide)

Part (a)

P(acute angled) = (n - 4)/[4(n - 1)], whenever n is even.

P(acute angled) = (n + 1)/[4(n - 2)], whenever n is odd.

Part (b)

P(right angled) = 3/(n - 1), whenever n is even

P(right angled) = 0, whenever n is odd

For an explanation, refer to the solution posted by Harry in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution	Harry	2011-08-15 01:00:49
re(2): computer findings for triangles through 50-gons	Charlie	2011-08-14 17:21:57
re: computer findings for triangles through 50-gons	Charlie	2011-08-14 17:08:52
computer findings for triangles through 50-gons	Charlie	2011-08-14 16:58:33

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