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
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.