MathDB

15

Part of 1976 IMO Longlists

Problems(1)

Concurrency on coplanar triangles

Source:

1/3/2011
Let ABCABC and A′B′C′A'B'C' be any two coplanar triangles. Let LL be a point such that AL∣∣BC,A′L∣∣B′C′AL || BC, A'L || B'C' , and M,NM,N similarly defined. The line BCBC meets B′C′B'C' at PP, and similarly defined are QQ and RR. Prove that PL,QM,RNPL, QM, RN are concurrent.
Eulerratiosymmetrygeometry