Triangle := a+b+c = 0; Median3 := m3-a/2 = c; Median2 := m2-c/2 = b; Median1 := m1 - b/2 = a; Hint2 := s*m2-r*m3 = b; Eq := s*solve(Median2,m2) - r*solve(Median3,m3) = b; Eq1 := subs(c=-(a+b),Eq); Eq2 := collect(lhs(Eq1)-b,[a,b]) = 0; E1 := coeff(lhs(Eq2),a) = 0; E2 := coeff(lhs(Eq2),b) = 0; Sol := solve({E1,E2},{r,s}); A := vector([x1,y1]): B := vector([x2,y2]): C := vector([x3,y3]): a := evalm(B-A); b := evalm(C-B); c := evalm(A-C); P := evalm(A + (2/3)*(a+(1/2)*b));