Circle theorems: chords

The Maths Habit

A straight bridge crosses a round pond. You are on an island at the centre. Which point of the bridge is nearest to you?

The middle of the bridge, straight out at 90°

A radius that meets a chord at 90° cuts the chord in half

Halve it

A chord of 14 cm 7 cm

What is the angle at M?

OABMOM meets AB at its midpoint 90°

Find the length of the chord AB.

OABM20 cm12 cm
the line from O at 90°
halves the chord
AM =16cm
Pythagoras: √(202 − 122)
AB = 2 × 16
AB = 32 cm

Find the length of the chord AB.

OABM29 cm21 cm
AM =20cm
Pythagoras: √(292 − 212)
AB = 2 × 20
AB = 40 cm

Find the length of the chord AB.

OABM20 cm12 cm
the line from O at 90°
halves the chord
AM =16cm
Pythagoras: √(202 − 122)
AB = 2 × 16
AB = 32 cm

Find the length of the chord AB.

OABM34 cm16 cm
AM =30cm
Pythagoras: √(342 − 162)
AB = 2 × 30
AB = 60 cm

Circle theorems: chords worksheet, page 1

Answer sheet

OABM

  1. AB = 24 cm and OM = 5 cm. Find the radius. 13 cm

  2. Two chords in a circle are the same length. What is true about their distances from the centre? They are equal

  1. OA is 15 cm and OM is 9 cm. Find AB.

    AB = 24 cm
    OABM

  2. OA is 17 cm and the chord AB is 16 cm. Find OM.

    OM = 15 cm
    OABM

  3. The chord AB is 40 cm and OM is 15 cm. Find the radius.

    25 cm
    OABM
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