How to define a central angle and find the measure of its intercepted arc; how to describe the intercepted arcs of congruent chords.
How to describe the effect of a reflection, how to describe the effect of the ordered pair rules (x,y) -> (-x, y),(x,y) -> (x, -y), (x,y) -> (y, x).
How to describe the unit circle. How to draw the unit circle and label its parts. How to strategize about finding coordinates on the unit circle.
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 calculate the measure of an inscribed angle.
How to define a secant; how to find the length of various secants in circles.
How to derive the formula to calculate the area of a sector in a circle.
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.