The figure shows a triangle ABC
with the circumcircle O and incenter I. D and E are the
midpoints of the arcs AB and BC, respectively. F is a point on
the circumcircle O, FD and AB meet at G, FE and BC meet at H.
Prove that points G, I, and H are collinear. See also:
Artwork
of Problem
669
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 illstructured 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.
