How to calculate the measure of an inscribed angle.
How to define circumscribed and inscribed circles and polygons relative to each other.
How to prove that an angle inscribed in a semicircle is a right angle; how to solve for arcs and angles formed by a chord drawn to a point of tangency.
How to find the length of tangent segments drawn to a circle from the same point.
How to calculate the area between a square and an inscribed circle.
How to prove that opposite angles in a cyclic quadrilateral are congruent; how to prove that parallel lines create congruent arcs in a circle.
How to define the apothem and center of a polygon; how to divide a regular polygon into congruent triangles.
How to determine if two triangles in a circle are similar and how to prove that three similar triangles exist in a right triangle with an altitude.