**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.

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