Perpendicular Bisector of Chord
What is a Chord?
A chord is a line segment that joins two points on a circle.
When the two points of the circle are at opposite ends, the chord is at its longest, with the special name given to it - diameter.
Perpendicular Bisector of a Chord
One of the properties of the chord is that its perpendicular bisector will always pass through the centre of the circle.
To observe and investigate on this property, play around with the applet below, dragging points O, B and C, or dragging whole circle entirely. You may also wish to show/hide the midpoint of the chord and its perpendicular bisector.
Linking this to coordinate geometry, with given two points on the circle, one can locate the equation of the line in which the centre of the circle lies.
| Step 1: | Calculate the gradient of the chord. |
| Step 2: | Calculate the gradient of the perpendicular bisector () |
| Step 3: | Find the coordinates of the midpoint of the chord. |
| Step 4: | Find the equation of the perpendiculat bisector () |