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Problem 492. Cyclic Quadrilateral, Circle, Perpendicular, Parallel.
Level: High School, College, SAT Prep.

The figure shows a cyclic quadrilateral ABCD and a circle O. AEF is perpendicular to AC (E on the circle O and F on DB extended), DGH is perpendicular to BD (G on the circle O and H on AC extended), Prove that FH, BC, and EG are parallel.
Cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle.

Cyclic quadrilateral, Perpendicular, Side, Diagonal, Parallel
 

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? 
 

Mind Map: How to Solve It

 

 

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