Triangles and circles but not geometry part-1
Probability
Level
3
There is a 2n+1 sided regular convex polygon. Now triangles are made by joining the vertices of polygon . Find the number of right angled triangles formed.
The answer is 0.
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1 solution
Consider the polygon to be inscribed in a circle. Now any right triangle inscribed in a circle must have as its hypotenuse a diameter of the circle. But since the polygon has an odd number of sides, and hence vertices, none of the diagonals joining the vertices of the circle will be diameters of the circle. Thus 0 right triangles can be formed as described.