Problem 567: Right triangle, Incircle, Excircle, Collinear tangency
points.
Level: High School, College, Math Education.
The drawing shows a right triangle ABC. The incircle D is
tangent to AB and AC at G and H, respectively. The excircle E is
tangent to CB extended at F. Prove that F, G, and H are
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 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.
Problem Solving. Activate Flash plugin or Javascript and
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