How to define a circle and identify its main parts.
How to derive the formula to calculate the area of a circle.
How to derive the equation for a circle using the distance formula.
How to calculate the area between a square and an inscribed circle.
How to find the length of tangent segments drawn to a circle from the same point.
How to define a circle and a sphere using the word locus.
How to define circumscribed and inscribed circles and polygons relative to each other.
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 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.
How to define a chord; how to describe the effect of a perpendicular bisector of a chord and the distance from the center of the circle.
How to define perimeter and calculate it for squares, rectangles, and circles.
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 derive the formula to calculate the area of a sector in a circle.
How to define arc length and how it is different from arc measure; how to calculate the length of an arc.
How to calculate the circumference of a circle.
How to prove the surface area of a cylinder formula.
How to derive the formula for the area of an annulus.
How to calculate the surface area of any cone explaining lateral surface area.
How to calculate the surface area of a cylinder joined to a cone.
How to compare the volume of a cone and a cylinder and how to calculate the volume of a cone given the radius and height.