Mock AIME 1 2007-2008 Problems/Problem 11
Problem
is inscribed inside such that lie on , respectively. The circumcircles of have centers , respectively. Also, , and . The length of can be written in the form , where and are relatively prime integers. Find .
Solution
From adjacent sides, the following relationships can be derived:
$\begin{align*} DC &= EC + 1\\ AE &= AF + 1\\ BD &= BF + 2 \end{align*}$ (Error compiling LaTeX. ! Package amsmath Error: \begin{align*} allowed only in paragraph mode.)
Since , and , . Thus, . . Thus, . Thus, the answer is .
See also
Mock AIME 1 2007-2008 (Problems, Source) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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