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Product of Ratios (Posted on 2008-09-08) Difficulty: 2 of 5
Let ABC be an arbitrary triangle with circumradius R, incenter I, and inradius r.
Let IA, IB, and IC be the excenters of ABC lying on the bisectors of interior angles A, B, and C respectively.

What is the value of the following product of ratios ?


    |IIA|     |IIB|     |IIC|      r
   ------- x ------- x ------- x ---
    |IA|      |IB|      |IC|      R

See The Solution Submitted by Bractals    
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Solution The Geometer's Sketchpad Answer (spoiler) Comment 1 of 1
4

Now prove it.

  Posted by Charlie on 2008-09-08 14:58:29
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