Posts tagged 'medians'

F.6 Centroid

The three medians AM_A, BM_B, CM_C joining the vertices of triangle ABC to the midpoints of the opposite sides concur at the centroid G = X(2), which divides each median in a 2 : 1 ratio and has homogeneous barycentric coordinates 1 : 1 : 1.

F.13 Compare Triangles in Circles

For a family of triangles ABC inscribed in a fixed circle of radius R sharing a fixed chord AB = c (with central angle 2*phi where sin(phi) = c/(2R)), the area K decomposes into the signed sum of three central isosceles triangles: K = (1/2) c h_c + (1/2) a h_a - (1/2) b h_b.