Creation of this applet was inspired by a problem from the 2006 Irish Mathematical Olympiad that was [url=http://www.cut-the-knot.org/wiki-math/index.php?n=MathematicalOlympiads.IrMO2006Problem2]posted on one of Cut-The-Knot's Wiki Pages[/url].

If a [color=#9900ff][b]point [/b][/color][i][color=#9900ff][b]P[/b][/color] [/i]lies on one leg of an isosceles triangle with [color=#1e84cc][b]vertex angle [i]A[/i][/b][/color] and leg length [i]k [/i]so that 0 < [i]AP < k,[/i] and if [color=#9900ff][b]another point [i]Q[/i][/b][/color] lies on the other leg of this isosceles triangle so that [i]AQ[/i] = [i]k - AP[/i], then the circumcircle of [b][color=#38761d]triangle [i]APQ[/i][/color][/b] will ALWAYS pass through the [b]CIRCUMCENTER[/b] of the isosceles triangle.