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The figure shows a triangle ABC with a
transversal DEF (F on the extension of AC). O1, O2,
O3, and O4 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 O4O2O3. are similar, (3) O1,
O2, O3, O4, 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.
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Problem 548: Triangle, Circle, Concyclic Points,
iPad Apps, Typography.