Sunday, April 5, 2020

Dynamic Geometry 1468: Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii

Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

Dynamic Geometry 1468: Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii, Step-by-step Illustration, iPad.

2 comments:

  1. https://photos.app.goo.gl/BAb6FnZVGoRYxj5j6

    Let 2p= perimeter of triangle ABC
    Draw diameter KL of circle O (see sketch)
    We have KL=MK+ML=2R….(1)
    Note that M is the midpoint of TTa and TcTb ( see sketch)
    In trapezoid EcEbTbTc we have MK=1/2(Rc+Rb)…(2)
    In trapezoid ITEaTa we have ML=1/2(Ra-r)…. 3)
    Combine (1), (2) and (3) we have 2R=1/2(Rc+Rb)+1/2(Ra-r)
    And 4R+r= Ra+Rb+Rc

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  2. Draw NOMP perpendicular to BC (N,M on O). M midpoint of TcTb => MN middle line of trapez
    MN = (Rc+Rb)/2 (1)
    BTa=TC => MTa=MT. Draw NS perpnd to EaTa From congruece of tr
    MP+r=Ra-MP (2)
    From (1) and (2) Ra+Rb+Rc=4R+r

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