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Circles for AQA GCSE Maths

Circles

This page covers the following topics:

1. Radius and diameter of a circle
2. Circumference of a circle
3. Area of a circle
4. Chords and tangents of a circle

The radius of a circle is the distance between the centre of a circle and the edge. The diameter of a circle is the distance between two edges of a circle passing through the centre. The diameter is double the size of the radius.

Radius and diameter of a circle

The circumference of a circle can be calculated using the following formula: C = 2ฯ€r, where r is the radius of a circle.

Circumference of a circle

The area of a circle is given by the formula: A = ฯ€rยฒ, where r is the radius of the circle.

Area of a circle

A chord of a circle is a line segment inside a circle that joins one point on a circle to another. The largest possible chord of a circle is the diameter. A tangent of a circle is a line segment that touches a point from the outside of a circle at exactly one point. The radius at the point at which a tangent is drawn is perpendicular to the tangent.

Chords and tangents of a circle

1

Calculate the area of a circle with radius 5 cm.

A = ฯ€(5 cm)ยฒ = 25ฯ€ cmยฒ = 78.5 cmยฒ (to 3 significant figures).

Calculate the area of a circle with radius 5 cm.

2

Define the chord of a circle.

A chord of a circle is a line segment inside a circle that joins one point on a circle to another.

Define the chord of a circle.

3

Find the value of x in the given diagram.

The angle between the tangent and radius is 90ยบ.
So, x = 180 โˆ’ 90 โˆ’ 30 = 60ยบ.

Find the value of x in the given diagram.

4

Given that the angle between the two radii is 90ยบ, show that the shaded shape is a square.

The angle between each tangent and each radius that touches it is 90ยบ.
The sum of the interior angles of a quadrilateral is 360ยบ, therefore the missing angle has a value of 360 โˆ’ (90 + 90 + 90) = 90ยบ.
Since all the sides of the shape have equal length and all interior angles are 90ยบ, the shape has been shown to be a square.

Given that the angle between the two radii is 90ยบ, show that the shaded shape is a square.

5

Given that r = 8 cm, calculate the circumference of the given circle.

C = 2ฯ€(8 cm) = 16ฯ€ cm = 50.3 cm (to 3 significant figures).

Given that r = 8 cm, calculate the circumference of the given circle.

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