**Circle Theorems for who? IGCSE, GCSE, **

**“Subtends” – what does that mean?
**

**The grand theorem**

**Proof**(not required for exams but not too difficult)

**So what then follows:**Angles on the same segment, Angle in a semi-circle, Cyclic quadrilaterals, Alternate segment theorem

**Then Add Tangents to a Circle…
**

**… and now we can answer questions (Tips)**

**Approach**: Maths teachers like to start easy Maths and then build it up to make it more complex. But sometimes it can be best to start at the top. We will start with the hard Circle Theorem and from then on it gets easier and easier.

**Subtends**: First a difficult word that only Maths teachers and examiners use. Students normally use simpler language.

Maths Teachers say | Students may say |

Chord BC subtends an angle of 48º with A | Chord BC makes an angle of 48º with A |

Arc BC subtends an angle of 48º with A | Or just: angle BAC is 48º |

**The grand theorem **(Play with the geogebra applet)** **