Midpoint of a Chord

Midpoint of a Chord

For a chord of a circle, the midpoint is the foot of the perpendicular from the centre to the chord.

For centre $$O(h,k)$$ and chord line:

$$Ax+By+C=0$$

the midpoint is:

$$M=\left(h-\frac{A(Ah+Bk+C)}{A^2+B^2},k-\frac{B(Ah+Bk+C)}{A^2+B^2}\right)$$

Usage

- Used to find the midpoint of a chord directly from its equation.