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.

 

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."
 

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? 
 

Problem Solving. Activate Flash plugin or Javascript and reload to view the Mind Map of How to Solve It, Interactive Mind Map, Elearning.