Problem 500. Circle, Diameter, Chord, Perpendicular, Measure. Level: High School, College, SAT Prep. The drawing shows a circle of diameter AB. The chords AC and BD meet at E. EF is perpendicular to AB. FC and BD meet at G. If DE = 5 and EG =3, find the measure of BG.       Geometry problem solving 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." How to Solve It, Interactive 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 Help. To see a note: Hover over a yellow note button. To Fold/Unfold: click a branch. To Pan: click and drag the map canvas. Problem Solving. Activate Flash plugin or Javascript and reload to view the Mind Map of How to Solve It, Interactive Mind Map, Elearning. Recent Additions