What (not-often-seen) theorem is dynamically being illustrated in the applet below? [br](Feel free to move any of the points wherever you'd like!)
[b]Theorem: [/b] [br][br]Suppose triangle [i]ABC [/i]has [b][color=#ff00ff]angle [i]B = [/i]60 degrees.[/color][/b][br]Suppose the bisector of [color=#38761d][b]angle [i]C[/i][/b][/color] meets [i]AB[/i] at [i]K[/i]. [br]Suppose the bisector of [color=#1e84cc][b]angle [i]A[/i][/b][/color] meets [i]BC[/i] at [i]L[/i]. [br][br]If this is the case, then [color=#9900ff][b][i]AK[/i] + [i]CL[/i] = [i]AC[/i].[/b][/color] [br][br][url=https://twitter.com/gogeometry]Antonio Gutierrez[/url] posted a [url=https://twitter.com/gogeometry/status/817005032449130496]tweet[/url] about this problem.