The figure shows a triangle ABC with a
transversal DEF (F on the extension of AC). O_{1}, O_{2},
O_{3}, and O_{4} are the circumcenters of triangles
ABC, BDE, ECF, and ADF, respectively. Prove that (1) the circumcircles
of triangles ABC, BDE, ECF, and ADF meet at a point G, (2) Triangles ABC
and O_{4}O_{2}O_{3}. are similar, (3) O_{1},
O_{2}, O_{3}, O_{4}, and G are concyclic points
(lie on a same circle).
Geometric Art using iPad or Mobile Apps
Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.
A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers. See also:
Original problem
548.
