The tangents from an external point are equal in length | Maths

Starter quiz

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

'54' ✓
The size of the angle labelled $b$ ° is ______°.

'50' ✓
∠ATC = 51° ∠ABT is subtended by the chord AT. The size of the angle labelled $e$ ° is ______°.

'51' ✓
∠PEF is subtended by the chord PF. ∠PFE is subtended by the chord PE. Find ∠EPD (in degrees).

48°

62°

70° ✓

90°

Not enough information.
The size of angle $c$ ° is ______°.

'72' ✓
Find the size of angle $d$ ° (in degrees).

'144' ✓

A triangle is formed on the circle from a segment of a tangent, a radius and another line segment. The size of angle $a$ ° is ______°.

'67' ✓
Points T and U are points where two separate tangents intersect the circle. Find the size of angle $b$ ° (in degrees).

'74' ✓
Points G and H are points where two separate tangents intersect the circle. The size of angle $c$ ° is ______°.

'55' ✓
Points Q and P are points where two separate tangents intersect the circle. The size of the angle labelled $d$ ° is ______°.

'50.5' ✓
Points J and K are points where two separate tangents intersect the circle. The size of angle $e$ ° is ______°.

'96' ✓
Points L and N are points where two separate tangents intersect the circle. ∠LMN = 118°. $g$ ° = ______°.

'56' ✓

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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 think that all circle theorems are about angles.

Circle theorems can be about angles or lengths in diagrams containing a circle.

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.
Equidistant - Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.