Difference between revisions of "2019 CIME I Problems/Problem 8"

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Revision as of 00:28, 12 October 2020

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 $BF \cdot DE.$