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Area Man Who Talks a Lot About Teaching Teaches His First Full Day in >10
Years
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I have taught demo and observational classes regularly since I left
full-time teaching but yesterday was the first time I taught every class
for the day. L...
3 years 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.