The angle in a semicircle is a right angle | Maths | Quizalize & Oak National Academy

Starter quiz

A chord has endpoints of A and B. Where on the circle must points A and B lie?

At the centre of the circle

On a tangent to the circle

On the circumference of the circle ✓

Inside the circle

Outside the circle
The size of the angle labelled $x$ ° on this 20-point geoboard is ______°.

'108' ✓
The size of the angle labelled $y$ ° on this 20-point geoboard is ______°.

'36' ✓
The size of the angle labelled $z$ ° on this 20-point geoboard is______°.

'54' ✓
What is the size of the angle subtended by the chord AC (in degrees)?

'36' ✓
The size of the angle labelled $m$ ° is ______°.

'68' ✓

Exit quiz

Find the size of angle $a$ ° on this 8-point geoboard (in degrees).

2°

8°

20°

45° ✓

360°
Find the size of angle $b$ ° on this 8-point geoboard (in degrees).

$180° - 45°$

$\big({{180° - 45°}\over2}\big)$ ✓

$45°\over2$

67.5° ✓

135°
The size of the angle labelled $c$ ° on this 8-point geoboard is ______°.

'135' ✓
The size of the angle $(b+d)$ ° on this 8-point geoboard is ______°.

'90' ✓
The size of the angle labelled $x$ ° is ______°.

'76' ✓
Chord AB has length of 4 cm. The length of chord BC is ______ cm (2 d.p.).

'23.66' ✓

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Lesson Details

Key learning points

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments
Theorems can be thought of as puzzles to solve, you are showing how to find a result
In order to use this theorem, you may need to draw a diagram or add more information to an existing one

Common misconception

Pupils may over-generalise the circle theorem by assume that all triangles that are inscribed in a circle are right-angled.

The triangle is only right-angled if one of its angles is subtended by the diameter. This also means that if the triangle is right-angled, then its hypotenuse is the diameter of the circle.

Keywords

Subtended - An angle can be subtended by a line segment or curve. The legs of the subtended angle meet the endpoints of the line segment or curve.
Arc - An arc of a circle is part of the circle’s circumference.
Chord - A chord is any line segment joining two points on the circumference of a circle.
Diameter - The diameter of a circle is any line segment that starts and ends on the circumference of the circle and passes through the centre of the circle.