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Mock AIME 6 2006-2007 Problems/Problem 9

Revision as of 09:24, 23 November 2023 by Tomasdiaz (talk | contribs) (Created page with "==Problem== <math>ABC</math> is a triangle with integer side lengths. Extend <math>\overline{AC}</math> beyond <math>C</math> to point <math>D</math> such that <math>CD=120</...")
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Problem

$ABC$ is a triangle with integer side lengths. Extend $\overline{AC}$ beyond $C$ to point $D$ such that $CD=120$. Similarly, extend $\overline{CB}$ beyond $B$ to point $E$ such that $BE=112$ and $\overline{BA}$ beyond $A$ to point $F$ such that $AF=104$. If triangles $CBD$, $BAE$, and $ACF$ all have the same area, what is the minimum possible area of triangle $ABC$?

Solution

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