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Recommended investigations

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

Equal Areas: Construct a circle with five equal regions that do not intersect at the circle's center.

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.

Changes in the Circumference: Explore how changing the diameter of a circle affects its circumference.

Maximal Volume of a Cone: Determine the sector of a circle that will produce a cone with maximum volume.

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.

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.

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.

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

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

Circling the Coordinate Plane: Given coordinates of the endpoints of a circle's diameter, find the circle's area.

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

Circles & Triangle: Find the relationship between the circumradius of a triangle and the radii of the circles that pass through the triangle's vertices.

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