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

Labels:
Ceva's theorem,
concurrent,
excircle,
Gergonne,
semiperimeter,
tangency point,
triangulo

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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