Chord with Given Midpoint for a Circle at Origin

Rarely Tested

Chord with Given Midpoint for a Circle at Origin

For:

$$x^2+y^2=a^2$$

if the midpoint of the chord is $$(x_1,y_1)$$, then the chord is:

$$xx_1+yy_1=x_1^2+y_1^2$$

Usage

- Used directly when the circle is centred at the origin and the midpoint of the chord is known.

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