Tribute to a very special woman...

The following was written by one of my daughters. It expresses what each of
us feels every day after six years...
A little boy walks by alone on the sidewa...
1 month ago
The answer is 3/4.
ReplyDeleteObserve that if A, B, and C are three points on a circle, then the points lie on a common semicircle if and only if the center of the circle does not lie inside the triangle ABC.
Let A, B, and C be three randomly selected points on the circle. Let a, b, and c be the points on the circle that are directly opposite to A, B, and C, respectively.
Using these six points we form eight triangles: ABC, ABc, AbC, Abc, aBC, aBc, abC, and abc. Observe that exactly two of these triangles contain the center of the circle. But each triangle has the same likelihood of containing the center.
Therefore, the probability that A, B, and C lie on a common semicircle is 6/8, or 3/4.