Circle Geometry
Students will understand that:
- A tangent to a circle intersects the circle in only one point and is perpendicular to the radius of the circle at that point.
- A line through the centre of a circle that is perpendicular to a chord bisects the chord.
- Inscribed angles subtended by the same arc are congruent and their measures are one-half the measure of the central angle subtended by the same arc.
- Geometric properties of angles and chords in a circle and tangents to a circle can be used to determine angle and line segment measures.
Essential Questions:
- What is a radius? What is a tangent? What is a point of Tangency?
- What does perpendicular mean? What is a chord? What is a perpendicular bisector?
General Outcomes:
- Students will use direct or indirect measurement to solve problems.
- Students will solve problems and justify the solution strategy using circle properties
- The perpendicular from the centre of a circle to a chord bisects the chord.
- The measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc.
- The inscribed angles subtended by the arc are equal.
- A tangent to a circle is perpendicular to the radius at the point of tangency.
- Students will solve problems and justify the solution strategy using circle properties