Rational Trigonometry/10

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Circles
Circles have
 * a quadrance (the square of the radius)
 * a center
 * diameters
 * chords
 * tangents

On a circle of quadrance K, for a random chord of quadrance Q, if we make a triangle with a random point X on the circle, then the spread at point X is Q over 4K.

Subtended Spread
$$ r = 4s(1-s) $$

Equal Produts
Two chords

$$Q_1 \cdot Q_2 = Q_3 \cdot Q_4$$