G-C.A. Understand and apply theorems about circles

• Two Wheels and a Belt

G-C.A.1. Prove that all circles are similar.

• Similar circles

G-C.A.2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

• Neglecting the Curvature of the Earth
• Right triangles inscribed in circles I
• Right triangles inscribed in circles II
• Tangent Lines and the Radius of a Circle

G-C.A.3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

• Circumcenter of a triangle
• Circumscribed Triangles
• Inscribing a circle in a triangle I
• Inscribing a circle in a triangle II
• Inscribing a triangle in a circle
• Locating Warehouse
• Opposite Angles in a Cyclic Quadrilateral
• Placing a Fire Hydrant

G-C.A.4. Construct a tangent line from a point outside a given circle to the circle.

• Tangent to a circle from a point