000RM.dvi

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

X = (0:1:1)

Y = (1:0:1)

Z = (1:1:0)

G = (1:1:1)