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
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)..
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.
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 90^{o}.
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.