What (not-well-known) theorem is dynamically being illustrated below? [br][color=#000000][b]Note:[/b][/color] Each circle that will soon appear will be tangent to every other item (circle or segment) it touches. [br][color=#000000][b]Also note: [/b][/color] The segments that will soon appear will be tangent to each smaller circle it touches. [br][br]How on Earth would you try to write what you see into words? (Try it!) [br][color=#000000][b]Feel free to move the LARGER white points anywhere you'd like! [/b][/color]
[color=#000000][b]Theorem:[/b][/color][br][br]Suppose there is an equilateral triangle whose incircle is drawn and has three smaller circles that are drawn inside this triangle so that each one is tangent to the incircle and 2 of the triangles' sides. [b][color=#000000]F[/color][color=#000000]rom ANY POINT on the equilateral triangle's incircle[/color][/b], if tangent segments are drawn, from this point, tangent to each of the three other smaller circles, then the sum of the lengths of the two smaller tangents is equal to the length of the largest tangent. [br]