2004 AMC 12B Problems/Problem 24

Problem

In $\triangle ABC$ , $AB = BC$ , and $\overline{BD}$ is an altitude. Point $E$ is on the extension of $\overline{AC}$ such that $BE = 10$ . The values of $\tan \angle CBE$ , $\tan \angle DBE$ , and $\tan \angle ABE$ form a geometric progression, and the values of $\cot \angle DBE, \cot \angle CBE, \cot \angle DBC$ form an arithmetic progression. What is the area of $\triangle ABC$ ?

$\mathrm{(A)}\ 16 \qquad\mathrm{(B)}\ \frac {50}3 \qquad\mathrm{(C)}\ 10\sqrt{3} \qquad\mathrm{(D)}\ 8\sqrt{5} \qquad\mathrm{(E)}\ 18$

Solution

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2004 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 23	Followed by Problem 25
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2004 AMC 12B Problems/Problem 24

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