Students discover the alternate segment theorem and angle between the radius and tangent of a circle.

Later, as learning progresses, they apply these theorems to work out unknown angles.

**Differentiated Learning Objectives**

- All students should be able to discover that a tangent and radius intersect at the circumference of a circle and are perpendicular.
- Most students should be able to discover that a tangent and radius intersect 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.