Geometry Problem

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

Click the figure below to see the complete problem 684.

## Wednesday, November 2, 2011

### Problem 684: Outer Nagel Point, Triangle, Excircles, Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem

Labels:
center,
Ceva's theorem,
concurrent,
excircle,
incircle,
Nagel theorem,
semiperimeter,
tangency point,
triangle

Subscribe to:
Post Comments (Atom)

AB':B'C = (s - a):(s - c)

ReplyDeleteCA':A'B = s:(s - a)

BC':C'A = (s - c): s

Product = 1

So AA', BB', CC' are concurrent (by Ceva)

Is there a solution using only projective geometry?

ReplyDelete