Geometry Problem 1375: Isosceles Triangle, Interior Cevian, Exradius, Excircle, Altitude to the Base.

Proposition

In the figure below, ABC is an isosceles triangle (AB = BC) with altitude BE = h. D is a point on AC, r1 is the exradius of the triangle ABD corresponding to AD and r2 is the exradius of the triangle DBC corresponding to BC. Prove that r2 - r1 = h.

BD is called an interior cevian of triangle ABC.
 

Geometry Problem 1375: Isosceles Triangle, Interior Cevian, Exradius, Excircle, Altitude to the Base, Sketch, iPad Apps
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Typography of problem 1375

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