The tangent at any point on a circle is perpendicular to the radius at that point | Maths

Starter quiz

The ______ is a line which intersects the circle exactly once.

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

'26' ✓
MY = 8 cm, OZ = 13 cm, ZM = 12 cm, OM = 5 cm. Find the distance MX.

5 cm

8 cm

12 cm ✓

13 cm

Not enough information.
The size of the angle labelled $m$ ° is ______° (in degrees).

'71' ✓
The size of the angle labelled $a$ ° is ______°.

'46' ✓
The angle subtended from arc AB at the circumference of the circle is 11°. Find ∠BOA (in degrees).

5.5°

11°

22° ✓

79°

169°

The size of the angle labelled $x$ ° on this 9-point geoboard is ______°.

'80' ✓
Find ∠OAB on this 9-point geoboard (in degrees).

40°

50° ✓

80°

90°

Not enough information.
Find ∠EFO on this 8-point geoboard (in degrees).

'90' ✓
Find ∠DEF on this 8-point geoboard (in degrees).

'45' ✓
Find the size of angle $x$ ° (in degrees).

'13' ✓
Find the size of angle $y$ ° (in degrees).

'79' ✓

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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

Pupils may assume that tangents can be drawn in slightly different directions at the same point on a circle.

The tangent at a point on a circle can only be drawn in one possible direction. The tangent is always perpendicular to the radius at that point.

Tangent - A tangent of a circle is a line that intersects the circle exactly once.
Chord - A chord is any line segment joining two points on the circumference of a circle.
Perpendicular - Two lines are perpendicular if they meet at right angles.