Geometry Problem

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## Friday, March 4, 2011

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

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## Friday, March 4, 2011

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

Online Geometry theorems, problems, solutions, and related topics.

Click the figure below to see the complete problem 590.

Zoom at: Geometry Problem 590

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Using the result of Problem 587,

ReplyDelete2(S2 + S3)

=r(b-c) + r(a-b)

=r(a-c)

=2S1

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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