Introduction to Circle Geometry

Task goals

• Name key parts of a circle, including the radius, diameter, and an arc.
• State and apply the four basic circle facts to find a missing angle in a numeric example (angle in a semicircle, tangent-radius angle, angles in the same segment, angle at the centre versus circumference).
• Complete each circle fact as a sentence (e.g. "the angle at the centre is ___ the angle at the circumference").
• Use one of the four circle facts to set up and solve a simple linear equation for an unknown angle.
• Explain or justify why a circle fact gives a particular result in a given situation, including why an alternative value is impossible.
• Use one of the four circle facts to set up and solve a harder linear equation, including expressions with brackets or negative coefficients, for an unknown angle.
• Critique a claim about circle angles with a supporting and a counter example, or reason through a multi-step problem that combines more than one circle fact.