This Demonstration provides four locators to change the shape of triangle
and to rotate the (blue) line
that goes through the point
. The result is true even if
is not inside the triangle; that is, even when
is not an acute triangle. Rotate
. The point in common mentioned in the statement of the problem is the intersection of the brown lines. This is problem 41 taken from the ninth International Mathematical Olympiad (IMO) held at Celtinje, Yugoslavia, July 2-13, 1967.
 D. Djukić, V. Janković, I. Matić, and N. Petrović, The IMO Compendium
, 2nd ed., New York: Springer, 2011.