Math 20P Polygon Angles Inscribed - Inscribed Angle Inscribed - Central Angle Perpendicular Chord Bisector Tangent to a Circle Prerequisite Skills

## Perpendicular Bisector to a Chord Circle Properties

Complete the Learning Strategy first to see the pattern, then read Circle Property to place what you understand in a mathematical context..

Circle Property

Learning Strategy

Perpendicular Bisector of a Chord Properties

1. If you have a line through the centre of the circle which is perpendicular to a given chord, then the line bisects the chord (cuts the chord into two equal segments)..
2. If you have a line through the centre of the circle which bisects the chord (cuts the chord into two equal segments), then the line is perpendicular to the chord.
3. If you have a line which is a perpendicular bisector of a given chord (cuts the chord into two equal segments and intersects the chord at a right angle), then that line will pass through the centre of the circle.

If you have any two of the above statements, then the third is true.

The following slideshow provides sample directions for the applet on the right.

Interactive Activity

• Move the point A inside of the circle.
• Move point B until segment BO bisects (cuts in half) chord CD.
• The angle between the radius and the bisected chord will be 90o.
• To change the size of the circle click SHIFT as you drag the circumference of the circle.
• Look at the chart below this one if you need additional explanation.