Geometry Problem 1140: Triangle, Circumcircle, Circle, Center, Collinear Points. Level: High School, SAT Prep, Honors Geometry, College, Math Education

In a triangle ABC of circumcircle O, a circle of center B cuts the circle O and AC at C₁, B₁, B₂, and A₁, respectively, (see figure below). The circumcircle of triangle AB₁C₁ cuts AB at C₂. The circumcircle of triangle A₂B₂C cuts BC at A₂. C₁C₂ and A₁A₂ meet at D. C₁B₁ and A₁B₂ meet at E. C₂B₁ and A₂B₂ meet at F. Prove that (1) Points B, D, and O are collinear; (2) Points B, E, and F are collinear. 

See also: Art 01

Mind Map: George P�lya's 1945 book, "How to Solve It"

George P�lya's 1945 book "How to Solve It, A new aspect of Mathematical Method", is a book describing methods of problem solving. It suggests the following steps when solving a mathematical problem: (1) First, you have to understand the problem. (2) After understanding, then make a plan. (3) Carry out the plan. (4) Look back on your work. How could it be better?
A mind map is a diagram used to visually organize information, knowledge, concepts or ideas.