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

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 $$r_1\cdot r_3\cdot r_5=r_2\cdot r_4\cdot r_6$$.

## Poster of the problem 1457 using iPad Apps

### Classroom Resource:Interactive step-by-step animation using GeoGebra

This step-by-step interactive illustration was created with GeoGebra.

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GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5.