Difference between revisions of "2019 CIME I Problems/Problem 8"
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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== | ||
+ | {{CIME box|year=2019|n=I|num-b=7|num-a=9}} | ||
+ | {{MAC Notice}} |
Latest revision as of 16:09, 13 October 2020
In parallelogram the circumcircle of
has center
and intersects lines
and
at
and
respectively
Let
and
be the midpoints of
and
respectively
Suppose that
and the height from
to
has length
Find the value of
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 |
The problems on this page are copyrighted by the MAC's Christmas Mathematics Competitions.