The Book of Lemmas Proposition 1 - Maple Help

The Book of Lemmas: Proposition 1

 Main Concept If two internally tangent circles touch at $A$, and if $\mathrm{BD}$, $\mathrm{EF}$ are parallel diameters in the circles (such that $\mathrm{BD}$ points in the same direction as $\mathrm{EF}$), then $\mathrm{ADF}$ is a straight line. Alternately, if two externally tangent circles touch at $A$, and if $\mathrm{DB}$, $\mathrm{EF}$ are parallel diameters in the circles (such that $\mathrm{DB}$ points in the same direction as $\mathrm{EF}$), then $\mathrm{DAF}$ is a straight line.

Adjust the sliders to change the radius of the inner circle and the angle of the diameters with respect to the horizontal axis. Also, drag the angles on the plot to change them.

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