000RM.dvi

25.3 Ceva Theorem 707

Example: Nagel point

IfX,Y,Zare the points of tangency of the excircles with the respective
sidelines, the linesAX,BY,CZintersect at the Nagel point.

A

B C

Z

X

Y

s−c s−b

s−a

s−b s−c

s−a Q

X =(0:s−b:s−c)

Y =(s−a:0:s−c)

Z =(s−a:s−b:0)

Q =(s−a:s−b:s−c)