Circles & Triangles

Find the relationship between the circumradius of a triangle and the radii of the circles that pass through the triangle’s vertices.

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.

Equal Areas

Construct a circle with five equal regions that do not intersect at the circle’s center.

Tangential Circles

Compare the area and circumference of a circle inscribed in a region between two intersecting circles.