Circle theorems
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 6 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Eight rules, each with a name
- The words
- Centre and circumference
Read the transcript of the teaching part
Last time
Before we start: last time, in Angles, polygons and symmetry, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Eight rules, each with a name
Circle theorems look like a lot to learn. But there are only eight, and each has a short name and a picture. In the exam you must name the theorem you use, because the reason is worth a mark of its own. Let us learn the eight with a worked example for each.
The words
A radius goes from the centre to the edge. A chord joins two points on the edge. A diameter is the longest chord. A tangent touches the circle at one point only. An arc is part of the edge. A segment is the region between a chord and an arc. A cyclic quadrilateral has all four corners on the circle.
Centre and circumference
Theorem one: the angle at the centre is twice the angle at the circumference, standing on the same arc. If the angle at the circumference is thirty-five degrees, the angle at the centre is seventy. Theorem two: the angle in a semicircle is ninety degrees. This is the same theorem, with a straight diameter.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Angles in circles · Tangents and chords.
The whole chapter: Circle Theorems.
Chapter 22: Circle theorems
- Circle theorems 6 min
Also for IGCSE Maths 0580
Which topics come up most in IGCSE Maths 0580 past papers, counted from every paper since 2004.