A GCSE maths resource that can be used to revise and consolidate circle theorems.
There are 18 double-sided flash cards with questions on:
basic circle facts
the angle in a semi-circle
angles at the centre and the circumference of a circle
angles in the same segment
alternate segment theorem
The sheets need to be photocopied or printed back to back, so the questions match up with the answers on the reverse. The cards can then be put together into a set and used for independent revision or with a friend asking the questions.
Sample questions and answers from the revision cards:
F) O is the centre of the circle.
Q1. Name lines OX and OY. Answer: OX and OY are both radii (plural of radius).
Q2. Name the shaded area. Answer: The shaded area between them is called a sector.
Q1. What is a cyclic quadrilateral? Answer: A cyclic quadrilateral is one in which all four vertices touch the circumference of a circle.
Q2. State the rule for angles in a cyclic quadrilateral. Answer: The opposite angles sum to 180°.
Aside from circle theorems, suggest some other angle rules you may need to know when given a question on angles in circles.
Angles in a triangle sum to 180˚.
Vertically opposite angles are equal.
Parallel line rules:
• corresponding angles are equal
• alternate angles are equal
• (co-)interior angles sum to 180˚.
Q1. What is a tangent? Answer: A tangent is a straight line which touches the circumference of a circle at just one point.
Q2. What angle does it make with a radius? Answer: It makes a right angle with the radius at that point.
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