When any three points are selected from a circle, what is the probability that they will form an obtuse-angled triangle?

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Shaswata Roy ·

Let ABC be a triangle , O the center of circumcircle and BB' a diameter.

Let's try and find out the probability that it is an acute angled triangle.(Since it involves less complications)

If ABC is acute angled then O will be included inside ΔABC.

(Using normal coordinate system with center as origin)For ΔABC to be acute A should lie in 2nd quadrant and C should lie in 3rd quadrant.

Hence probability that ΔABC is acute = 1/2*/12=1/4

Therefore probability that the triangle is obtuse = 3/4

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