Right angled triangle

Probability Level 5

How Many Right - angled triangles can be formed by joining the vertices of a 1000 - sided regular polygon.

Try my set : Let's play with polygons & circles


The answer is 499000.

Aniket Sanghi by Aniket Sanghi , 21, India

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1 solution

Spandan Senapati
Mar 4, 2017

Quite easy.The angle in a semicircle is always 90.So the figure obtained is a symmetric figure.Considering 2 points of thepolygon that lie on the circumscribed circles diameter we can get 499 2=998 triangles.But the 2 points can be selected in 500ways so we get 998 500=499000triangles

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Hey Spandan Bhaiya, Can we do it this way, that we can make ( 500 2 ) \dbinom{500}{2} rectangles, And each rectangle will have 4 triangles out og which none is common, ⟹ \implies Total number of triangles = 4 × ( 500 2 ) 4 \times \dbinom{500}{2} . Is the concept okay?

Md Zuhair - 3 years, 2 months ago

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