Wednesday, November 9, 2011

Problem 687: Triangle, Excircles, Tangency points, Tangent lines, Concurrent Lines

Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 687.

Online Geometry Problem 687: Triangle, Three Excircles, Tangency points, Tangent lines, Concurrent Lines.
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2 comments:

  1. Peter TranNovember 9, 2011 at 7:40 PM

    Let A’, B’, C‘ are contacting points of encircles to BC, AC and AB
    Per the result of problem 682, 3, B3 and C3 are Gergonne points
    AA3 will cut BC at A’ and A’B/A’C= (s-a)/(s-b)
    Similarly B’C/B’A=(p-a)/p-c) and C’A/C’B=(s-b)/(s-a)
    And A’B/A’C . B’C/B’A . C’A/C’B = 1
    So AA3, BB3 and CC3 are concurrent per Ceva’s Theorem
    Peter Tran

    ReplyDelete
  2. PravinNovember 12, 2011 at 3:35 AM

    Typos:
    rhs's of
    A’B/A’C= (s-a)/(s-b),
    B’C/B’A=(p-a)/p-c)and
    C’A/C’B=(s-b)/(s-a)

    to be corrected as

    (s-c)/(s-b),
    (s-a)/(s-c)and
    (s-b)/(s-a)respectively

    ReplyDelete

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