Monday, May 19, 2008

Geometry Problem 95



See complete Problem 95
Similar Triangles, Inradii, Parallel. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.
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1 comment:

  1. tricycleAugust 7, 2008 at 8:45 PM

    Just saw the problem on the Mathematica Blog and followed the Mathematica Demo at
    http://demonstrations.wolfram.com/TheRadiiOfFourIncircles/
    So I wondered why it was true. Placing the radii of the incircles to the tangent points on BC and using similar triangles makes it clear:
    r/BC=r1/BE =r2/EG =r3/GC=(r1+r2+r3)/(BE+EG+GC).
    Since (BE+EG+GC=BC), r = r1+r2+r3.

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