Difference between revisions of "2017 USAJMO Problems/Problem 3"

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==Problem==
 
==Problem==
 
(<math>*</math>) Let <math>ABC</math> be an equilateral triangle and let <math>P</math> be a point on its circumcircle. Let lines <math>PA</math> and <math>PB</math> intersect at <math>D</math>; let lines <math>PB</math> and <math>CA</math> intersect at <math>E</math>; and let lines <math>PC</math> and <math>AB</math> intersect at <math>F</math>. Prove that the area of triangle <math>DEF</math> is twice that of triangle <math>ABC</math>.
 
(<math>*</math>) Let <math>ABC</math> be an equilateral triangle and let <math>P</math> be a point on its circumcircle. Let lines <math>PA</math> and <math>PB</math> intersect at <math>D</math>; let lines <math>PB</math> and <math>CA</math> intersect at <math>E</math>; and let lines <math>PC</math> and <math>AB</math> intersect at <math>F</math>. Prove that the area of triangle <math>DEF</math> is twice that of triangle <math>ABC</math>.
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==Solution==
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{{MAA Notice}}
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==See also==
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{{USAJMO newbox|year=2017|num-b=2|num-a=4}}

Revision as of 19:13, 19 April 2017

Problem

($*$) Let $ABC$ be an equilateral triangle and let $P$ be a point on its circumcircle. Let lines $PA$ and $PB$ intersect at $D$; let lines $PB$ and $CA$ intersect at $E$; and let lines $PC$ and $AB$ intersect at $F$. Prove that the area of triangle $DEF$ is twice that of triangle $ABC$.

Solution

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See also

2017 USAJMO (ProblemsResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5 6
All USAJMO Problems and Solutions
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