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2019 CIME I Problems/Problem 8

Revision as of 23:28, 11 October 2020 by Icematrix2 (talk | contribs) (Created page with "In parallelogram <math>ABCD,</math> the circumcircle of <math>\triangle BCD</math> has center <math>O</math> and intersects lines <math>AB</math> and <math>AD</math> at <math>...")
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In parallelogram $ABCD,$ the circumcircle of $\triangle BCD$ has center $O$ and intersects lines $AB$ and $AD$ at $E$ and $F,$ respectively$.$ Let $P$ and $Q$ be the midpoints of $AO$ and $BD,$ respectively$.$ Suppose that $PQ=3$ and the height from $A$ to $BD$ has length $7.$ Find the value of $BF \cdot DE.$

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