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:

${\mathrm{AO}}^2$ + ${\mathrm{BO}}^2$ + ${\mathrm{CO}}^2$ + ${\mathrm{DO}}^2$ = ${\mathrm{diameter}}^2$.

Arc Lengths:

${\mathrm{AO}}^2$            =      

${\mathrm{BO}}^2$            =      

${\mathrm{CO}}^2$            =      

${\mathrm{DO}}^2$            =      

∑                =      

${\mathrm{diameter}}^2$      =      

r ${\mathrm{AO}}^2$ + ${\mathrm{BO}}^2$ + ${\mathrm{CO}}^2$ + ${\mathrm{DO}}^2$ = ${\mathrm{diameter}}^2$

   $\mathbf{ }\mathbf{ }\mathit{x}\mathit{O} \left(\mathit{CD}\mathit{ }\right)\mathit{ }$                

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