Difference between revisions of "Mock AIME 4 2006-2007 Problems/Problem 4"

 
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Revision as of 10:46, 16 January 2007

Problem

Points $A$, $B$, and $C$ are on the circumference of a unit circle so that the measure of $\widehat{AB}$ is $72^{\circ}$, the measure of $\widehat{BC}$ is $36^{\circ}$, and the measure of $\widehat{AC}$ is $108^\circ$. The area of the triangular shape bounded by $\widehat{BC}$ and line segments $\overline{AB}$ and $\overline{AC}$ can be written in the form $\frac{m}{n} \cdot \pi$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.

Solution

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