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 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 define a tangent line; how to determine the angle a radius to a tangent forms.
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.