# Problem 669: Triangle, Circumcircle, Incenter, Midpoint, Collinear points, Mind Map

 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 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.
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