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

Question

Triangle ABC is stuck in a circle. Its points are on random areas on the circumference of the circle. What is the probability of the triangle covering the centre of the circle?

Answer 1

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.
Therefore the answer = 25%.