Intersecting Circles

Examine the relationship between two secants that pass through the intersections of two circles.

Circling the Coordinate Plane

Given coordinates of the endpoints of a circle’s diameter, find the circle’s area.

Equation of a Circle

Find the equation of a circle based on its radius, center, and locus of points.

Intersecting Chords

Determine a relationship between segments formed by the intersection of two chords of a circle.

Optimizing Triangles Using Radii

Find the triangles with maximum and minimum area if two sides of the triangle are determined by radii of the circle.

Area of a Sector

Determine a relationship between the area of a circle’s sector and the radius and central angle of the circle, and between the arc length of a sector and the radius and central angle of the circle.

Angles in a Circle

Investigate how the location of an angle’s vertex affects its relationship to the measure(s) of the arc(s) it intercepts.

Maximal Volume of a Cone

Determine the sector of a circle that will produce a cone with maximum volume.

Changes in the Circumference

Explore how changing the diameter of a circle affects its circumference.

Tangent Along the Diameter

Find a relationship between the area of a circle and the areas of the tangent circles along the circle’s diameter.