704 Routh and Ceva theorems
25.3 Ceva Theorem .................
Theorem 25.1(Ceva).LetX,Y,Zbe points on the linesBC,CA,AB
respectively. The linesAX,BY,CZare concurrent if and only if
BX
XC
·
CY
YA
·
AZ
ZB
=1.
If this condition is satisfied, the homogeneous barycentric coordi-
nates of the common point ofAX,BY,CZcan be written down by
combining the coordinates ofX,Y,Z.
Example: centroid
IfAX,BY,CZare the medians, the intersection is the centroidG:
1 1
1
1
1
1
A
B C
G
Z
X
Y