Problem 493. Right Triangle, Circumcircle, Perpendicular, Chord.
Level: High School, College, SAT Prep.
The figure shows a right triangle ABC
(angle B = 90 degrees) with the circumcircle C_{1} and
center O. From point D on C_{1}, perpendiculars DE and
DF are drawn to AC and AB, respectively. Lines BD and EF
intersect at G. Prove that OG is perpendicular to BD.
How to Solve It, Mind Map
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?

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