Cross Quotient

Given ∆ABC and points P and Q. Let QaQbQc be the cevian triangle of Q, and let PaPbPc be the cevian trriangle of P with respect to triangle QaQbQc. Then triangles ABC and PaPbPc are perspective, and the perspector is the Cross Quotient of P and Q.



QaQbQc = cevian triangle of point Q.
PaPbPc = cevian triangle of P wrt triangle QaQbQc.
R = Cross Quotient of P and Q = Perspector of triangles ABC and PaPbPc.