Random Triangles
Probability
Level
3
What is the probability that the triangle formed by three randomly chosen points on the circumference of a circle contains the circle's center?
1/π
5/9
1/2
1/4
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1 solution
Very difficult proof to explain. Very good video here
Suppose we chose 2 random diameters and 1 random point. It then follows that if we randomly chose an end of each of the diameters (2 ends for 2 lines is 4 paired possibilities) to be our 2nd and 3rd point, only 1 pair of those 4 possibilities allows point 3 to be across from the center as required. Thus the answer is 1/4