2020 CIME I Problems/Problem 9

Problem 9

Let $ABCD$ be a cyclic quadrilateral with $AB=6, AC=8, BD=5, CD=2$ . Let $P$ be the point on $\overline{AD}$ such that $\angle APB = \angle CPD$ . Then $\frac{BP}{CP}$ can be expressed in the form $\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .

Solution

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2020 CIME I (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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2020 CIME I Problems/Problem 9

Problem 9

Solution