A generalization double simson line

Define: Two pascal line merge into one 29-Aug-2013 Dao Thanh Oai, oaidt.slhpc@gmail.com Let A,B,C are on conic and F point. FA,FB,FC intersect the conic at A1,B1,C1. D also is on the conic. DB1 intersect Ac at B2; DA1 intersect BC at A2; DC1 intersect AB at C2. We have A2,B2,C2 and F are collinear. The line through A2,B2,C2,F is two pascal line merge into one. I named it is a line of D and F Remark: This line is generalization double Simson line Property 1: Let a conic, O is centre of the conic. A, B,C,N 1 ,N 2 are on the conic and O is midpoint of N 1 N 2 . D 1 ,D 2 are plane the conic. The line of D1 and N1 intersect meet the line of D2 and N2 at W. When N1 move on the conic => W draw a new conic. Construct: D 1 A,D 2 A intersect the conic at A 1D1 and A 1D2 . N 1 A 1D1 meet BC at A 2N1 ; N 2 A 1D2 meet BC at A 2N2 . A 2N2 D 2 meet A 2N1 D 1 at W. When N1 move on the conic => W draw a new conic. Property 2: Let seven points A,B,C,D,E,F,N are on a conic. K,H is on a plane of the conic. The line of K,N and the line of H,N (respectively the triangle ABC and the triangle DEF) intersect at W. When N move on the conic W draw a new conic. . intersect Ac at B2; DA1 intersect BC at A2 ; DC1 intersect AB at C2. We have A2 ,B2,C2 and F are collinear. The line through A2 ,B2,C2,F is two pascal line merge into one. I named it is a line of D and. Define: Two pascal line merge into one 29-Aug-2013 Dao Thanh Oai, oaidt.slhpc@gmail.com Let A, B,C are on conic and F point. FA,FB,FC intersect the conic at A1 ,B1,C1. D also is on the conic Remark: This line is generalization double Simson line Property 1: Let a conic, O is centre of the conic. A, B,C,N 1 ,N 2 are on the conic and O is midpoint of N 1 N 2 . D 1 ,D 2 are plane