30. Malfatti's Problem

Arguing through Malfatti's Problem: Draw three circles in a triangle. Each of these circles must be tangent to the two other circles and to two sides of the triangle. What kind of trouble does this get me into? Does it get me into enough trouble that I can find the heart of the problem?

In some places I have skipped a large number of steps. They are covered in the following worksheets: [list] [*] Inscribe a circle in a triangle: [url]http://www.geogebratube.org/material/show/id/30923[/url] [/list] [list] [*]Heron's Formula Proof: [url]http://www.geogebratube.org/material/show/id/31135[/url] [/list] [list] [*]Consider the trigonometric identity: [math] \;\;\; \sin²λ=\sin²α+\sin²β+2 \sinα \sin β \cos λ[/math] Multiplied by the half-perimeter s, it can be turned into the system of equations at the end of this worksheet. Ok but, [i]so what?[/i] See the trig supplement below. [/list] _______ Malfatti's Problem [b]→1. Identify and describe the constraints.[/b] 2. Solution: [url]http://www.geogebratube.org/material/show/id/32233[/url] 3. Trig Supplement: [url]http://www.geogebratube.org/material/show/id/31985[/url] These are self-study materials. Let me know how I can make them more useful to you.