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Problem 1105: Triangle, Incircle, Excircle, Circle, Cevian, Tangent, Congruence, Geometric Mean. Level: High School, SAT Prep, College Geometry

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In a triangle ABC (see the figure below) the incircle I is tangent to BC, AC, and AB at T1, T2, and T3. The excircle E corresponding to BC is tangent to AC, BC, and AB at F, G, and H, respectively. D is a point on AC so that the incircles of triangles ABD and BDC are congruent. Prove that BD is the geometric mean of AF and CF, that is, Formula to prove.

 

Geometry Problem 1105: Triangle, Incircle, Excircle, Cevian, Tangent, Congruence, Geometric Mean


 

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Last updated: Apr 1, 2015, by Antonio Gutierrez