semicircle chord cut v2 (applet)

This is a dynamic Geogebra applet that illustrates the solution to the problem posed in my blog entry on 30 July 2017

Drag point P manually or use the slider so that the x-coordinate of P changes in increments of 0.0001.  Observe the ratio of the area of the green region compared to area of semicircle - and when the ratio is 1/2, observe the interesting property of point P.  Tip: Select the slider for \({{\rm{x}}_{{\rm{P}}'}}\) and then use right and left arrows on keyboard.  You can then get a value for the x-coordinate of P accurate to 4 significant figures.

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