466.A Small Triangle Somewhere
★★★geometric probabilityCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
A point is chosen uniformly at random inside triangle . Find the probability that at least one of the triangles , , has area at most one quarter of the area of .
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The three sub-triangle areas are the barycentric coordinates of — they're nonnegative and sum to 1.
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