Tuesday, November 1, 2011

Problem 682: Gergonne External Point, Triangle, Excircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem

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

Click the figure below to see the complete problem 682.

Online Geometry Problem 682: Gergonne Point, Triangle, Incircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem
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1 comment:

  1. PravinNovember 2, 2011 at 6:32 PM

    AB'= C'A(each = s)
    B'C = CA'(each = s - b)
    C'B = BA'(each = s - c)
    Follows
    (AB'/B'C).(CA'/A'B).(BC'/C'A)
    =(AB'/C'A).(CA'/B'C).(BC'/A'B)
    = 1.1.1
    = 1
    Hence by Ceva's Theorem
    AA', BB', CC'are concurrent

    ReplyDelete

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