A [b]chord [/b]is a line segment that joins two points on a circle. [br]When the two points of the circle are at opposite ends, the chord is at its longest, with the special name given to it - [b]diameter[/b].

One of the properties of the chord is that [b]its perpendicular bisector will always pass through the centre of the circle[/b]. [br][br]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.[br][br]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.[br][br][table][tr][td][b]Step 1:[/b][/td][td]Calculate the gradient of the chord.[/td][/tr][tr][td][b]Step 2:[/b][/td][td]Calculate the gradient of the perpendicular bisector ([math]m_1\times m_2=-1[/math])[/td][/tr][tr][td][b]Step 3:[/b][/td][td]Find the coordinates of the midpoint of the chord.[/td][/tr][tr][td][b]Step 4:[/b][/td][td]Find the equation of the perpendiculat bisector ([math]y-y_1=m\left(x-x_1\right)[/math])[/td][/tr][/table]