Search Results for ""

The three points determined on three coplanar edges of a tetrahedron by the external bisecting planes of the opposite dihedral angles are collinear. Furthermore, this line ...

A Cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension). The condition for three general Cevians from the three ...

A triangle ABC formed by three circular arcs. By extending the arcs into complete circles, the points of intersection A^', B^', and C^' are obtained. This gives the three ...

Given a triangle DeltaABC and a point P not a vertex of DeltaABC, define the A^'-vertex of the circumcevian triangle as the point other than A in which the line AP meets the ...

A perimeter-bisecting segment of a polygon originating from the midpoint of one side. Each cleaver M_1C_1, M_2C_2, and M_3C_3 in a triangle DeltaA_1A_2A_3 is parallel to an ...

The complex structure of a point x=x_1,x_2 in the plane is defined by the linear map J:R^2->R^2 J(x_1,x_2)=(-x_2,x_1), (1) and corresponds to a counterclockwise rotation by ...

Four or more points P_1, P_2, P_3, P_4, ... which lie on a circle C are said to be concyclic. Three points are trivially concyclic since three noncollinear points determine a ...

Given a triangle, draw a Cevian to one of the bases that divides it into two triangles having congruent incircles. The positions and sizes of these two circumcircles can then ...

Conway triangle notation defines S=2Delta (1) where Delta is the area of a reference triangle, and S_phi=Scotphi. (2) This gives the special cases S_A = 1/2(-a^2+b^2+c^2) (3) ...

Consider a convex plane curve K with perimeter L, and the set of points P exterior to K. Further, let t_1 and t_2 be the perpendicular distances from P to K (with ...