Geometry and measuresGCSE Higher / IGCSE Extended

Equal chords of the same circle are the same perpendicular distance from the centre

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

  • Measure each distance at right angles to its chord. Conversely, chords equally distant from the centre are equal.

The theorem

Equal chords of the same circle are the same perpendicular distance from the centre.

Example 1

With numerical values

is the centre. and are equal chords. and are perpendicular to them. Find in cm.

Equal chords are equidistant from the centre.

Example 2

With algebra

is the centre. and are equal chords. and are perpendicular to them. Find . All lengths are in cm.

Equal chords are equidistant from the centre.
Substitute the value of .
Labelled lengths

Your turn

Question 1

Find in cm.

Check answer
Equal chords are equidistant from the centre.
Question 2

Find . All lengths are in cm.

Check answer
Equal chords are equidistant from the centre.
Substitute the value of .
Labelled lengths
Question 3

Find in cm.

Check answer
Equal chords are equidistant from the centre.
Question 4

Find . All lengths are in cm.

Check answer
Equal chords are equidistant from the centre.
Substitute the value of .
Labelled lengths
Question 5

Find in cm.

Check answer
Equal chords are equidistant from the centre.
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