// triangle-perpendicular-are-collinear-ex323.ggb 7.67s, 6.5s, 5.53s, 3.38s, 3.26s, 2.56s, 2.39s, 2.13s
// [v12^3*v10-v12*v10^3+v12^2*v9*v11-2*v12*v10*v9*v11-v10^2*v9*v11+2*v10^2*v11^2,v12^2*v10^2-v12*v10^3-v10^2*v9*v11+v10^2*v11^2,v12^2*v10*v9-v12*v10^2*v9-v10*v9^2*v11+v10*v9*v11^2,v12^2*v10*v11-v12*v10^2*v11-v12*v9^2*v11+v12*v9*v11^2,v12^2*v9^2-2*v12*v10*v9*v11+v10^2*v11^2,v12*v10*v9^2-2*v12*v10*v9*v11+v9^3*v11+v10^2*v11^2-v9^2*v11^2,v12*v10*v11^2-v10^2*v11^2-v9^2*v11^2+v9*v11^3,v12*v9^3*v11-v12*v9^2*v11^2-v10*v9^2*v11^2+v10*v9*v11^3,v10^2*v9^2*v11^2-2*v10^2*v9*v11^3+v10^2*v11^4,v10*v9^3*v11^2-2*v10*v9^2*v11^3+v10*v9*v11^4,v9^4*v11^2-2*v9^3*v11^3+v9^2*v11^4]
aa:=eliminate([-1*v14+v11+-1*v9,-1*v13+-1*v12+v10,-1*v15*v12+v16*v11+v15*v10+-1*v11*v10+-1*v16*v9+v12*v9,v15*v14+-1*v16*v13,-1*v18+v11+v10,-1*v17+-1*v12+v9,v19*v18+-1*v20*v17+-1*v19*v10+v17*v10+v20*v9+-1*v18*v9,-1*v19*v12+v20*v11,-1*v22+v12+-1*v9,-1*v21+v11+v10,v23*v22+-1*v24*v21+-1*v23*v12+v21*v12+v24*v11+-1*v22*v11,v23*v10+-1*v24*v9,-1*v25*v24+v26*v23+v25*v20+-1*v23*v20+-1*v26*v19+v24*v19,-1*v25*v12+v26*v11+v25*v10+-1*v11*v10+-1*v26*v9+v12*v9,-1*v27*v24+v28*v23+v27*v16+-1*v23*v16+-1*v28*v15+v24*v15,-1*v27*v12+v28*v11,v29*v10+-1*v30*v9,v29*v20+-1*v30*v19+-1*v29*v16+v19*v16+v30*v15+-1*v20*v15,-1+v31*v29*v28+-1*v31*v30*v27+-1*v31*v29*v26+v31*v27*v26+v31*v30*v25+-1*v31*v28*v25],revlist([v13,v14,v15,v16,v17,v18,v19,v20,v21,v22,v23,v24,v25,v26,v27,v28,v29,v30,v31]))