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Ceva's Theorem/Problems

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Contents

Introductory

I1

Problem

Suppose AB, AC, and BC have lengths 13, 14, and 15, respectively. If \frac{AF}{FB} = \frac{2}{5} and \frac{CE}{EA} = \frac{5}{8}, find BD and DC.

Solution

If BD = x and DC = y, then 10x = 40y, and {x + y = 15}. From this, we find x = 12 and y = 3.

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