1981 IMO Problems/Problem 1
is a point inside a given triangle . are the feet of the perpendiculars from to the lines , respectively. Find all for which
We note that is twice the triangle's area, i.e., constant. By the Cauchy-Schwarz Inequality,
with equality exactly when , which occurs when is the triangle's incenter, Q.E.D.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
|1981 IMO (Problems) • Resources|
|1 • 2 • 3 • 4 • 5 • 6||Followed by|
|All IMO Problems and Solutions|