Geometry Problem 1373: Isosceles Triangle, Exterior Cevian, Inradius, Exradius, 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 CA extended, r1 is the inradius of the triangle DAB and r2 is the exradius of the triangle DBC corresponding to BC. Prove that r1 + r2 = h.

BD is called an exterior cevian of triangle ABC.
 

Geometry Problem 1373: Isosceles Triangle, Exterior Cevian, Inradius, Exradius, Altitude, Sketch, iPad Apps
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Typography of problem 1373

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Isosceles triangle
Inradius
Exradius
Cevian
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