Three points are chosen uniformly at random from the perimeter of circle. The probability that the triangle formed by these is acute can be expressed as ab where a and b are coprime positive integers. What is the value of a+b?

Answer 1

Place point A anywhere on the circle.
Draw a diameter from point A.

Now place point B. It lies on one side of that diameter.

There is a 50% chance that point C lies on the same side of the diameter as point B.

Now, if C is at the end of the diameter, ABC is a right triangle.

ABC is acute if C lies on the opposite side of the diameter from B.

The chance of that is 1/2, so a+b=3

Answer 2

its wrong

Answer 3

its five...

let the points be abc,
put "a" anywhere. you can place b at diametrically opposite or not (1/2) then if they are not diametrical opposite then there are two sides where we can place c.and one gives acute and other gives obtuse... so 1/2
so 1/2*1/2=1/4 so 5..:P :)