Saturday, April 16, 2016

Geometry Problem 1208: Triangle, Circle, Excircle, Excenter, Diameter, Perpendicular, Equal Areas

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.


Click the figure below to view more details of problem 1208.

Geometry Problem 1208: Triangle, Circle, Excircle, Excenter, Diameter, Perpendicular, 90 Degrees, Equal Areas
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2 comments:

  1. Peter TranApril 16, 2016 at 2:45 PM

    http://s22.postimg.org/8bjm3kpox/pro_1208.png

    Draw line B’FC’ //BC and tangent to circle E at F ( see sketch)
    Circle E become incircle of triangle AB’C’
    Perform homothetic transformation, center A and scaling factor= AB/AB’=AC/AC’=AG/AF
    In this transformation, tri. AB’C’ become tri ABC , circle E become incircle I of tri. ABC, F become G
    So G is the tangent point of incircle I of triangle ABC to BC
    So BG=DC=p – AC ( p= haft perimeter of triangle ABC)
    Triangles BGF and FDC have same base and altitude so these triangles have same area.

    ReplyDelete
  2. Sumith PeirisApril 28, 2016 at 3:38 AM

    Do you have another proof for this Antonio?

    ReplyDelete

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