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 A_{1}, B_{1}, C_{1}. Let
r_{1}, r_{2}, r_{3}, r_{4}, r_{5},
r_{6} represent the length of the inradii of the triangles AB_{1}H, CB_{1}H, CA_{1}H, BA_{1}H, BC_{1}H, AC_{1}H. Prove that \(r_1\cdot r_3\cdot r_5=r_2\cdot r_4\cdot r_6\).

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Geometry Problems

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Ten problems: 1411-1420

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Triangle

Circle

Circumcircle

Triangle Centers

Altitude

Orthocenter

Perpendicular lines

Incenter, Incircle, Inradii

Orthic Triangle

Similarity, Ratios, Proportions

Dynamic Geometry

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