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Ceva's Theorem/Problems

From AoPSWiki

Contents

1 Introductory
- 1.1 I1
  - 1.1.1 Problem
  - 1.1.2 Solution

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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