Circle Geometry
Circles are rich with hidden relationships. The angle inscribed in a semicircle is always 90° — a theorem students can discover by measuring and then prove. Tangent lines are perpendicular to the radius at the point of contact. These properties connect geometry, measurement, and deductive reasoning in a way that few other topics do.
What students explore
Circles are rich with hidden relationships. The angle inscribed in a semicircle is always 90° — a theorem students can discover by measuring and then prove. Tangent lines are perpendicular to the radius at the point of contact. These properties connect geometry, measurement, and deductive reasoning in a way that few other topics do.
Key ideas
Identify and apply properties of chords, tangents, and arcs. Apply the inscribed angle theorem. Prove and apply properties: angle in a semicircle, tangent-radius relationship. Solve problems using circle geometry theorems.
Putting it together
Apply these ideas through worked examples, guided practice, and real-world problems.