2011 USAMO Problems/Problem 5
Problem
Let be a given point inside quadrilateral
. Points
and
are located within
such that
,
,
,
. Prove that
if and only if
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
First note that if and only if the altitudes from
and
to
are the same, or
. Similarly
iff
.
If we define , then we are done if we can show that S=1.
See also
2011 USAMO (Problems • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |