# Unit 13: Circles and Spheres

Essential Questions:
• What figures are always similar to each other?
• How are circles and Pythagorean Theorem related?
• Why are we still using triangles with circles?
• What does a circle become in three dimensions? What are the similarities and differences between that object and a circle?
Content:
• Definition of a circle.
• Representation of a circle on a coordinate plane - equation.
• Coordinate proofs for: angle inscribed in a semicircle is right, line through center of circle and midpoint of chord is perpendicular to the chord, distances between congruent chords and the center of the circle are equal.
• When can't we use coordinate proofs?
• Intersection of circles and lines.
• Using similarity theorems to prove circle theorems.
• Comparing circles to spheres.
• Surface area and volume of a sphere.
Skills and Processes:
• Generate equation of a circle using distance formula.
• Write equation of a circle given center and radius.
• Write equation of a circle given a center and a point on the radius.
• Proving circle theorems with and without coordinate proofs.
• Solving systems of circles and lines.
• Calculate volume and surface area of spheres.