Given an acute triangle. Find an inscribed triangle whose perimeter is minimum.
Let tPQR denote triangle PQR.
Let ABC be the acute triangle and A'B'C'
the inscribed triangle with A', B', and
C' on sides opposite vertices A, B, and
C respectively.
For the perimeter of tA'B'C' to be a
minimum, then tA'B'C' must satisfy
tAB'C' ~ tA'BC' ~ tA'B'C ~ tABC.
The orthic triangle of tABC (AA', BB',
and CC' are altitudes of tABC) is the
only triangle that does.

Posted by Bractals
on 20100425 15:03:17 