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Geometry Problem 959. Triangle, Sides Ratio 4:1, Inradius, Exradius, Cevian, Mean Proportional, Geometric Mean

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The figure below shows a triangle ABC so that AC = 4AB and AD = AB (D on AC). Prove that BD is the mean proportional between the inradius and the exradius corresponding to BC.
 

Geometry Problem 959: Triangle, Sides Ratio 4:1, Inradius, Exradius, Cevian, Mean Proportional, Geometric Mean

 

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