Geometry and measuresGCSE Higher

The perpendicular from the centre of a circle to a chord bisects the chord

Recognise the theorem, follow two examples, then try five questions.

  • Conversely, the perpendicular bisector of a chord passes through the centre. is perpendicular to .

The theorem

The perpendicular from the centre of a circle to a chord bisects the chord.

Example 1

With numerical values

is the centre. is perpendicular to chord . Find in cm.

The perpendicular from the centre bisects the chord.

Example 2

With algebra

is the centre. is perpendicular to chord . Find . All lengths are in cm.

The perpendicular from the centre bisects the chord.
Substitute the value of .
Labelled lengths

Your turn

Question 1

Find in cm.

Check answer
The perpendicular from the centre bisects the chord.
Question 2

Find . All lengths are in cm.

Check answer
The perpendicular from the centre bisects the chord.
Substitute the value of .
Labelled lengths
Question 3

Find in cm.

Check answer
The perpendicular from the centre bisects the chord.
Question 4

Find . All lengths are in cm.

Check answer
The perpendicular from the centre bisects the chord.
Substitute the value of .
Labelled lengths
Question 5

Find in cm.

Check answer
The perpendicular from the centre bisects the chord.
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