In a triangle ABC of circumcircle O, a circle of
center B cuts the circle O and AC at C_{1}, B_{1}, B_{2}, and A_{1},
respectively, (see figure below). The circumcircle of triangle AB_{1}C_{1}
cuts AB at C_{2}. The circumcircle of triangle A_{2}B_{2}C cuts BC at A_{2}.
C_{1}C_{2} and A_{1}A_{2} meet at D. C_{1}B_{1} and A_{1}B_{2} meet at E. C_{2}B_{1} and A_{2}B_{2} 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 Pólya's 1945 book,
"How to Solve It"
George Pólya'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.
