The Book of Lemmas Proposition 11 - Maple Help

The Book of Lemmas: Proposition 11

 Main Concept If two chords in a circle, $\mathrm{AB}$ and $\mathrm{CD}$, intersect at right angles in a point O, not being the center, then: ${\mathrm{AO}}^{2}$ + ${\mathrm{BO}}^{2}$ + ${\mathrm{CO}}^{2}$ + ${\mathrm{DO}}^{2}$ = ${\mathrm{diameter}}^{2}$.

Click on the plot to create points $A$ and ${B}^{}$ on the circle's perimeter. Adjust the slider to move the x-coordinate, xO , of the point $O$, where the two lines intersect. Note that the sum of the squares of distances between points $A$, ${B}^{}$, $C$ and D is equal to the square of the diameter of the circle.

 Arc Lengths: ${\mathrm{AO}}^{2}$            =       ${\mathrm{BO}}^{2}$            =       ${\mathrm{CO}}^{2}$            =       ${\mathrm{DO}}^{2}$            =       ∑                =         ${\mathrm{diameter}}^{2}$      =         r ${\mathrm{AO}}^{2}$ + ${\mathrm{BO}}^{2}$ + ${\mathrm{CO}}^{2}$ + ${\mathrm{DO}}^{2}$ = ${\mathrm{diameter}}^{2}$

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