Go Geometry Problem 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.
 

Problem 220: Right triangle, altitude, inradius
 

 

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