Wednesday, November 2, 2011

Problem 683: Nagel Point, Triangle, Excircles, Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem

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

Click the figure below to see the complete problem 683.

Online Geometry Problem 683: Nagel Point, Triangle, Excircles, Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem
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1 comment:

  1. c.t.e.o.December 22, 2011 at 1:55 PM

    Right tr similar to each other
    EcC'A to EbB'A, EbB'C to EaA'C, EaA'B to EcC'B
    AB'/C'A=EbB'/EcC'
    A'C/B'C=EaA'/EbB'
    BC'/BA'=EcC'/EaA'
    (AB'/C'A)(A'C/B'C)(BC'/BA')=(EbB'/EcC')(EaA'/EbB')(EcC'/EaA')
    (BC'/C'A)(AB'/B'C)(CA'/BA')=1
    AA', BB', CC' are concurent by ceva theorem

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