Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.
Click the figure below to see the complete problem 682.
Tuesday, November 1, 2011
Problem 682: Gergonne External Point, Triangle, Excircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem
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AB'= C'A(each = s)
ReplyDeleteB'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