Circle Theorems

Question 1

Tangent to a circle

Answer 1

A tangent to a circle is a straight line that touches the circle at exactly one point.

A tangent to a circle is perpendicular to the radius of the circle at the point of intersection.

Question 2

Perpendicular bisector of a chord

Answer 2

The perpendicular bisector of a chord will always pass through the centre of the circle.

Question 3

Angle in a semi-circle

Answer 3

The angle in a semi-circle is always a right angle.

Question 4

Multiple perpendicular bisectors to chords

Answer 4

If there are two or more chords in a circle, their perpendicular bisectors will always intersect each other at the centre of the circle.

Question 5

How do you find the shortest distance from centre to chord?

Answer 5

Identify / find the radius of circle

Find the length of the chord

Halve it to find one side of triangle

Use Pythagoras to find the shortest
distance from centre to chord.

Question 6

How do you find the length of
tangent to circle from a
point?

Answer 6

Identify / find the radius of circle

Find the distance from point to centre of circle

Use Pythagoras to find the length of
tangent

Question 7

How do you find the centre of a
circle when given 3 points on
the circle?

Answer 7

Find the equations of the perpendicular
bisectors of any two of the chords.

Find the coordinates of intersection of the perpendicular bisectors.

This coordinate is the centre of the circle.