Program of Studies

Topic 5: Circles and Coordinate Geometry

General Outcome: Develop and apply the geometric properties of circles and polygons to solve problems.

Specific Outcomes:

• 5.1 Use technology and measurement to confirm and apply the following properties to particular cases:
  • 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 same arc are congruent
  • the angle inscribed in a semicircle is a right angle
  • the opposite angles of a cyclic quadrilateral are supplementary
  • a tangent to a circle is perpendicular to the radius at the point of tangency
  • the tangent segments to a circle, from any external point, are congruent
  • the angle between a tangent and a chord is equal to the inscribed angle on the opposite side of the chord
  • the sum of the interior angles of an n-sided polygon is (2n – 4) right angles [or 180(n - 2)^o].
  [PS, R, T, V]

• 5.2 Prove the following general properties, using established concepts and theorems:
  • the perpendicular bisector of a chord contains the centre of the circle
  • the angle inscribed in a semicircle is a right angle
  • the tangent segments to a circle from any external point are congruent.
  [PS, R, CN]
  

• 5.3 Solve problems, using a variety of circle properties and relevant trigonometric ratios, and justify the solution strategy used.
  [PS, R, V]