Geometry Problem 1457: Altitudes, Circles, Similarity, Product of the Inradii Lengths

Let AH_A, BH_B, CH_C be the altitudes of a triangle ABC. The extensions of AH_A, BH_B, CH_C intersect the circumcircle O at A₁, B₁, C₁. Let r₁, r₂, r₃, r₄, r₅, r₆ represent the length of the inradii of the triangles AB₁H, CB₁H, CA₁H, BA₁H, BC₁H, AC₁H. Prove that \(r_1\cdot r_3\cdot r_5=r_2\cdot r_4\cdot r_6\).

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Static Diagram of problem 1457

Dynamic Geometry 1457: Altitudes, Circles, Similarity, Product of the Inradii Lengths. Using GeoGebra

Poster of the problem 1457 using iPad Apps

Poster of Problem 1457, Altitudes, Circles, Similarity, Product of the Inradii Lengths, GeoGebra, iPad

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