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Difference between revisions of "2019 AIME II Problems/Problem 1"
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==Problem==
 
Two different points, <math>C</math> and <math>D</math>, lie on the same side of line <math>AB</math> so that <math>\triangle ABC</math> and <math>\triangle BAD</math> are congruent with <math>AB = 9</math>, <math>BC=AD=10</math>, and <math>CA=DB=17</math>. The intersection of these two triangular regions has area <math>\tfrac mn</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.
 
Two different points, <math>C</math> and <math>D</math>, lie on the same side of line <math>AB</math> so that <math>\triangle ABC</math> and <math>\triangle BAD</math> are congruent with <math>AB = 9</math>, <math>BC=AD=10</math>, and <math>CA=DB=17</math>. The intersection of these two triangular regions has area <math>\tfrac mn</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.
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==Solution==

Revision as of 16:33, 22 March 2019

Problem

Two different points, $C$ and $D$, lie on the same side of line $AB$ so that $\triangle ABC$ and $\triangle BAD$ are congruent with $AB = 9$, $BC=AD=10$, and $CA=DB=17$. The intersection of these two triangular regions has area $\tfrac mn$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

Solution

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