Links to Syllabus

Synthetic Geometry:

Prior Knowledge: (JC OL)
Definition 27; The perpendicular bisector of a segment [AB] is the line through the midpoint of [AB], perpendicular to AB.
Proposition 10: Each point on the perpendicular bisector of a segment [AB] is equidistant from the ends.
Construction 2: Perpendicular bisector of a segment, using only compass and straight Edge.

(JC HL)
Definition 41: A cyclic quadrilateral is one whose vertices lie on some circle.
Corollary 5: If ABCD is a cyclic quadrilateral, then opposite angles sum to 180◦.

(LC OL)
Theorem 21 (2): The perpendicular bisector of a chord passes through the centre.
Proposition 17: If a circle passes through three non-collinear points A, B, and C, then its centre lies on the perpendicular bisector of each side of the triangle ABC.
Definition 43: The circumcircle of a triangle ABC is the circle that passes through its vertices. Its centre is the circumcentre of the triangle, and its radius is the circumradius.
Construction 16: Circumcentre and circumcircle of a given triangle, using only straight- edge and compass.

Extension Tasks:
Denition 41: A cyclic quadrilateral is one whose vertices lie on some circle.
Corollary 5: If ABCD is a cyclic quadrilateral, then opposite angles sum to 180.

Coordinate Geometry:
Recognise that (x-h)^2 + (y-k)^2 = r^2 represents the relationship between the x and y coordinates of points on a circle with centre (h, k) and radius r.