Circle theorems: angle in a semicircle

The Maths Habit

  1. O is the centre. Find x.

    124°xOx = 62°

  2. O is the centre. Find x.

    x47°Ox = 94°

  3. O is the centre. Find x.

    x38.5°Ox = 77°

AB goes through the centre. Which angle is biggest: the one at P, at Q or at R?

PQRAB All the same: 90°

The angle in a semicircle is 90°

What is the angle at C?

OABCAB is a diameter 90°

Is AB a diameter?

The angle at C is 80° No

AB is a diameter. Find x.

38°xABCO
Angle C =90°
angle in a semicircle
x = 180 −90−38
x =52°

AB is a diameter. Find x.

x66°ABCO
Angle C =90°
angle in a semicircle
x = 180 −90−66
x =24°

AB is a diameter. Find x.

38°xABCO
Angle C =90°
angle in a semicircle
x = 180 −90−38
x =52°

AB is a diameter. Find x.

xxABCO
Angle C =90°
angle in a semicircle
x + x = 90, so 2x = 90
x =45°

Circle theorems: angle in a semicircle worksheet, page 1

Answer sheet

  1. AB is a diameter of length 10 cm. C is on the circle and AC = 6 cm. Find BC.

    8 cm

  2. A triangle has sides 5 cm, 12 cm and 13 cm. Will it fit in a semicircle of diameter 13 cm?

    Yes: 5² + 12² = 13²

  1. AB is a diameter of the circle. Find angle x.

    x = 56°
    ABC34°x

  2. AB is a diameter of the circle. Find x.

    x = 16
    ABC2x + 103x

  3. A, B and C lie on a circle. Angle ACB is 86°. Is AB a diameter? Explain how you know.

    No: it would be 90°
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