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 referred 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, through A or C, 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.