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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| + | {{USAJMO newbox|year=2017|num-b=2|num-a=4}} | ||
Revision as of 18:13, 19 April 2017
Problem
(
) Let 
be an equilateral triangle and let 
be a point on its circumcircle. Let lines 
and 
intersect at 
; let lines and 
intersect at 
; and let lines 
and 
intersect at 
. Prove that the area of triangle 
is twice that of triangle .
Solution
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
See also
| 2017 USAJMO (Problems • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAJMO Problems and Solutions | ||
