Bisection of Chords (Edexcel A-Level Mathematics): Flashcards

A line segment with both endpoints on the circle.

$M = ((x_1 + x_2)/2, (y_1 + y_2)/2)$

A line that is perpendicular and passes through midpoint.

It is equidistant from the endpoints of a segment.

Midpoint $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$

$m = (y_2 - y_1) / (x_2 - x_1)$

It is the negative reciprocal of the chord's slope.

$y - y_1 = m(x - x_1)$

The centre is equidistant from both endpoints of the chord.

The perpendicular bisector of a chord passes through the centre.