Circles for OCR GCSE Maths
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.
The circumference of a circle can be calculated using the following formula: C = 2πr, where r is the radius of a circle.
The area of a circle is given by the formula: A = πr², where r is the radius of the 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.
Calculate the area of a circle with radius 5 cm.
A = π(5 cm)² = 25π cm² = 78.5 cm² (to 3 significant figures).
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.
Find the value of x in the given diagram.
The angle between the tangent and radius is 90º.
So, x = 180 − 90 − 30 = 60º.
Given that the angle between the two radii is 90º, show that the shaded shape is a square.
The angle between each tangent and each radius that touches it is 90º.
The sum of the interior angles of a quadrilateral is 360º, therefore the missing angle has a value of 360 − (90 + 90 + 90) = 90º.
Since all the sides of the shape have equal length and all interior angles are 90º, the shape has been shown to be a square.
Given that r = 8 cm, calculate the circumference of the given circle.
C = 2π(8 cm) = 16π cm = 50.3 cm (to 3 significant figures).
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