Friday, March 4, 2011

Problem 590: Triangle, Incenter, Incircle, Tangency Point, Midpoint, Areas.

Geometry Problem
Click the figure below to see the complete problem 590.

Geometry Problem 590. <br />Triangle, Incenter, Incircle, Tangency Point, Midpoint, Areas..
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Posted by Antonio Gutierrez at 11:58 AM
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2 comments:

  1. PravinMarch 4, 2011 at 8:27 PM

    Using the result of Problem 587,
    2(S2 + S3)
    =r(b-c) + r(a-b)
    =r(a-c)
    =2S1

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  2. ShanksterMay 14, 2011 at 3:58 PM

    I cheated, using a 3,4,5 right triangle and graph paper. Using Cartesian coordinates and Pythagorean relationships, the numbers work just fine. I intend to try a couple other 'friendly' triangles as well, but I'm sure the intent here is to develop a more general solution based on Euclid.

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