Difference between revisions of "1977 USAMO Problems/Problem 2"
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== Problem == | == Problem == | ||
<math> ABC</math> and <math> A'B'C'</math> are two triangles in the same plane such that the lines <math> AA',BB',CC'</math> are mutually parallel. Let <math> [ABC]</math> denotes the area of triangle <math> ABC</math> with an appropriate <math> \pm</math> sign, etc.; prove that | <math> ABC</math> and <math> A'B'C'</math> are two triangles in the same plane such that the lines <math> AA',BB',CC'</math> are mutually parallel. Let <math> [ABC]</math> denotes the area of triangle <math> ABC</math> with an appropriate <math> \pm</math> sign, etc.; prove that | ||
| − | <cmath> 3([ABC] | + | <cmath> 3([ABC]+ [A'B'C']) = [AB'C'] + [BC'A'] + [CA'B']+ [A'BC]+[B'CA] + [C'AB].</cmath> |
== Solution == | == Solution == | ||
Revision as of 14:17, 17 September 2012
Problem
and 
are two triangles in the same plane such that the lines 
are mutually parallel. Let ![$[ABC]$](http://latex.artofproblemsolving.com/d/3/3/d33cc80fa8f093e155c5be46d2e5d9da3d7e1ef5.png)
denotes the area of triangle with an appropriate 
sign, etc.; prove that
![\[3([ABC]+ [A'B'C']) = [AB'C'] + [BC'A'] + [CA'B']+ [A'BC]+[B'CA] + [C'AB].\]](http://latex.artofproblemsolving.com/5/8/b/58b0b0c6ba5c2cb0d7264799fd86e5385a1e5919.png)
Solution
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See Also
| 1977 USAMO (Problems • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
