Thursday, July 24, 2008

Elearn Geometry Problem 140

 Triangle, excircle, semiperimeter

See complete Problem 140
Triangle, Excircle, Tangent, Semiperimeter. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

3 comments:

  1. A circle O tangent to BC at F.
    We have :AD=AE , BD=BF & CE=CF.
    p=(AB+AC+BC)/2
    p=(AB+AC+BF+CF)/2
    p=(AB+AC+BD+CE)/2
    p=(AD+AE)/2
    p=AD=AE

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  2. When you say CE=CF and BD=BF you are using the same principle you are trying to prove. That a point is equal distant from the two tangent points. How about:

    angle AEO and angle ADO are right angles because a tangent is perpendicular to a radius
    AO = AO by reflexive property
    OD = OE =r
    so triangle AOD is congruent to triangle AEO
    by hypotenuse leg.
    and AD = AE by CPCTC

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  3. To Dan May (about problem 140).
    The goal of the problem is not to prove that AD = AE. It is to prove that both are equal to the semiperimeter p of the triangle ABC!

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