3 points are randomly chosen on a circle. Find the probability that they are vertices of an acute angled triangle?

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3 points are randomly chosen on a circle. Find the probability that they are vertices of an acute angled triangle?
posted Oct 23, 2018

This question can be converted to what is the probability that 3 points chosen at random on the circle will make a triangle that includes the centre of the circle. Because only if the triangle has the centre in it, it will be acute triangle.
Now if we imagine 2 lines passing through the centre of the circle taken at random we have 4 different possibilities for picking 2 points on the circle (the order of chosen points won't matter). Now no matter where we pick our third point to be, only 1 of the 4 possible configuration will have the centre in it.

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