[color=#000000]Creation of this applet was inspired a [url=http://www.cut-the-knot.org/m/Geometry/BuratinoPascal.shtml]problem posted[/url] on Alexander Bogomolny's website: [url=http://www.cut-the-knot.org/]Cut-The-Knot.org[/url]. [/color][b][br][br][color=#9900ff]Suppose P is a point[/color] [/b][color=#000000]in the interior of [/color][color=#6aa84f][b]any triangle. [/b][/color][color=#000000][br]Draw lines through [/color][color=#9900ff][b]P[/b][/color][color=#000000] that each line is parallel to a side of the triangle. (There are 3 such lines.) [br][br][b]The 6 points at which these lines meet the triangle's sides WILL ALWAYS lie on a conic section. [/b] [br][br]Try it! Slide the slider and then move the purple point around. [br]Do you get different types of conic sections? [br][/color][color=#1e84cc](You can use the blue slider to adjust the size of the blue angle.) [br][br][/color][color=#000000]How can you formally prove what this applet informally illustrates?[/color]