TriangleCurve Command

TriangleCurve[<Point P>,<Point Q>,<Point R>,<Equation in A,B,C>]

creates implicit polynomial, whose equation in barycentric coordinates with respect to points P, Q,R is given by the fourth parameter; the barycentric coordinates are refered to as A,B,C.

Example: If P,Q,R are points, TriangleCurve[P,Q,R,(A-B)*(B-C)*(C-A)=0] gives a cubic curve consisting of the medians of the triangle PQR.

Example: TriangleCurve[A,B,C,A*C=1/8] creates a hyperbola such that tangent to this hyperbola splits triangle ABC in two parts of equal area.

Note: The input points can be called A, B or C, but in this case you cannot use e.g. x(A) in the equation, because A is interpreted as the barycentric coordinate.