An Application of the Gergonne-Euler Theorem
An Application of the Gergonne-Euler Theorem
Let the intersection of lines and be denoted . Let the line through point P and parallel to the line be denoted by [P, ].
g
h
g⋂h
g
g
Let ABC and A'B'C' be two triangles. Let , , and . Let , , and . Then XX', YY', and ZZ' are concurrent.
X=BC⋂B'C'
Y=CA⋂C'A'
Z=AB⋂A'B'
X'=[A,BC]⋂[A',B'C']
Y'=[B,CA]⋂[B',C'A']
Z'=[C,AB]⋂[C',A'B']