Original creativity and design in the app below by [url=https://www.geogebra.org/u/stevephelps]Steve Phelps[/url].

Move the [b]LARGE POINT [i]P[/i] [/b]to various locations around the circle. Each time you do, [br][list=1][*]Press the [b][color=#cc0000]Make Segment[/color][/b] button. [/*][*]Drag the segment you just made so its endpoint that originally touched the horizontal axis now touches the open-holed point on the right. (See quick screencast below.) [/*][*]Repeat steps (1) - (2) numerous times. Get as many segments dragged to the right as you can. [/*][*]Use the [b]PEN tool[/b] to draw a curve that connects the other endpoints of the segments that do not touch the horizontal axis. [/*][/list]