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

(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 <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>E</math> and <math>F,</math> respectively<math>.</math> Let <math>P</math> and <math>Q</math> be the midpoints of <math>AO</math> and <math>BD,</math> respectively<math>.</math> Suppose that <math>PQ=3</math> and the height from <math>A</math> to <math>BD</math> has length <math>7.</math> Find the value of <math>BF \cdot DE.</math>
 
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>E</math> and <math>F,</math> respectively<math>.</math> Let <math>P</math> and <math>Q</math> be the midpoints of <math>AO</math> and <math>BD,</math> respectively<math>.</math> Suppose that <math>PQ=3</math> and the height from <math>A</math> to <math>BD</math> has length <math>7.</math> Find the value of <math>BF \cdot DE.</math>
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==See also==
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{{CIME box|year=2019|n=I|num-b=7|num-a=9}}
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{{MAC Notice}}

Latest revision as of 16:09, 13 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 $BF \cdot DE.$

See also

2019 CIME I (Problems • Answer Key • Resources)
Preceded by
Problem 7 		Followed by
Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
All CIME Problems and Solutions

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