1977 USAMO Problems/Problem 2
Problem
and
are two triangles in the same plane such that the lines
are mutually parallel. Let
denote the area of triangle
with an appropriate
sign, etc.; prove that
Hint
Let the parallel lines be parallel to the
, and choose arbitrary origin. Then we can define
and so, by the area of a triangle formula, it suffices to prove an algebraic statement that is readily shown to be true.
See Also
1977 USAMO (Problems • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 | ||
All USAMO Problems and Solutions |
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