Creation of this applet was inspired by the the calendar problem (11/2/2016) that appeared in [url=http://www.nctm.org/]NCTM[/url]'s November 2016 issue of the [url=http://www.nctm.org/publications/mathematics-teacher/][i]Mathematics Teacher[/i] magazine[/url]. [br][br]"In right triangle [i]ABC[/i],[color=#0000ff][b] [i]CD[/i] is the bisector[/b][/color] of [color=#666666][b]right angle [i]ACB[/i][/b][/color], [color=#9900ff][b][i]CM[/i] is the median to the hypotenuse[/b][/color], and [color=#980000][b][i]CP [/i]is the altitude to the hypotenuse[/b][/color]. Prove [i][color=#0000ff][b]CD[/b][/color][/i] [color=#ff00ff][b]bisects[/b][/color] angle [i]PCM[/i]. " [br][br]This applet informally illustrates what this calendar problem is asking you to prove. [br][br]Can you formally prove what this applet informally illustrates?