Let AHA, BHB, CHC be the altitudes of a triangle ABC. The extensions of AHA, BHB, CHC 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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Ten problems: 1411-1420
Incenter, Incircle, Inradii
Similarity, Ratios, Proportions
HTML5 and Dynamic Geometry
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