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

Online Geometry Problems

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 about triangle, circumcircle, midpoint, incenter, collinear points

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.

Online Geometry


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