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Difference between revisions of "2021 JMPSC Invitationals Problems/Problem 10"

(Created page with "==Problem== A point <math>P</math> is chosen in isosceles trapezoid <math>ABCD</math> with <math>AB=4</math>, <math>BC=20</math>, <math>CD=28</math>, and <math>DA=20</math>. I...")
(No difference)

Revision as of 15:07, 11 July 2021

Problem

A point $P$ is chosen in isosceles trapezoid $ABCD$ with $AB=4$, $BC=20$, $CD=28$, and $DA=20$. If the sum of the areas of $PBC$ and $PDA$ is $144$, then the area of $PAB$ can be written as $\frac{m}{n},$ where $m$ and $n$ are relatively prime. Find $m+n.$

Solution

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