The proof of a theorem from geometry is dynamically being illustrated here. [br]Which theorem is it? And how does this applet informally illustrate its proof? [br](Feel free to move the points anywhere you'd like!)
[color=#000000][b]Theorem:[/b][/color][br]If 2 chords intersect inside a circle, then the product of the 2 segments of one chord = the product of the 2 segments of the other chord. [br][br]This applet shows it true. Here's how: [br][br]1) Both [color=#ff00ff][b]pink angles[/b][/color] are congruent since they are [color=#ff00ff][b]2 inscribed angles[/b][/color] that intercept the same [color=#ff00ff][b]pink arc[/b][/color]. [br]2) Both [color=#1e84cc][b]blue angles[/b][/color] are congruent since they are [color=#1e84cc][b]2 inscribed angles[/b][/color] that intercept the same [color=#1e84cc][b]blue arc[/b][/color]. [br]3) Thus, the two triangles shown are similar by AA~ Theorem.[br]4) Since corresponding sides of similar triangles are in proportion, we can write [math]\frac{a}{c}=\frac{d}{b}[/math]. [br]5) From this proportion, we can write [math]a\cdot b=c\cdot d[/math], which proves the theorem.