2021 CIME I Problems/Problem 1

Problem

Let $ABCD$ be a square. Points $P$ and $Q$ are on sides $AB$ and $CD,$ respectively $,$ such that the areas of quadrilaterals $APQD$ and $BPQC$ are $20$ and $21,$ respectively. Given that $\tfrac{AP}{BP}=2,$ then $\tfrac{DQ}{CQ}=\tfrac{a}{b},$ where $a$ and $b$ are relatively prime positive integers. Find $a+b$ .

Solution

$\boxed{123}$

2021 CIME I (Problems • Answer Key • Resources)
Preceded by First Problem	Followed by Problem 2
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2021 CIME I Problems/Problem 1

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