This lesson guides the class through the discovery of circle theorems involving tangents. The theorems include, the angle between a tangent and radius and angles in alternate segments.

Each circle theorem has an associated proof in the additional resources section. Once the theorems are discovered there is opportunity for students to consolidate their learning by calculating unknown angles.

**Differentiated Learning Objectives**

- All students should be able to discover that a tangent and radius intersecting at the circumference of a circle and perpendicular.
- Most students should be able to discover that a tangent and radius intersecting at the circumference of a circle and perpendicular and that angles in alternate segments are equal.
- Some students should be able to derive both theorems relating to tangents at the circumference of a circle and apply them to solve complex problems involving multiple circle theorems.