# AQA A Level Maths: Pure复习笔记3.2.3 Bisection of Chords

### Bisection of Chords

#### How can I find the equation of a perpendicular bisector?

• The perpendicular bisector of a line segment:
• is perpendicular to the line segment
• goes through the midpoint of the line segment

•  The midpoint and gradient of the line segment between points (x1, y1) and (x2, y2) are given by the formulae

•  The gradient of the perpendicular bisector is therefore

• The equation of the perpendicular bisector is the equation of the line with that gradient through the line segment's midpoint (see Equation of a Straight Line)

#### How can I use perpendicular bisectors to find the equation of a circle?

• A chord of a circle is a straight line segment between any two points on the circle

• The perpendicular bisector of a chord always goes through the centre of the circle

• If you know three points on a circle, draw two chords between them – the perpendicular bisectors of the chords will meet at the centre of the circle

• Now that you know the centre of the circle and a point on the circle you can write the equation of the circle

#### Exam Tip

• To find the point of intersection of two straight lines, set the equations of the lines equal to each other and solve.