Problem 220. Right Triangle, Altitude, Angle
Bisector, Distance, Arithmetic Mean

In a right triangle ABC, BD is the
altitude to the hypotenuse AC and r is the inradius. BE and BF
are the angle bisectors of angles ABD and DBC. Prove that r is
the arithmetic mean of the measures of the perpendiculars from E
and F to AB and BC respectively. View or post a solution.