Circles & Triangles

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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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Intersecting Circles

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

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Circling the Coordinate Plane

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

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Equation of a Circle

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

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Intersecting Chords

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

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Optimizing Triangles Using Radii

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

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Area of a Sector

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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.

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Angles in a Circle

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

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Maximal Volume of a Cone

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

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Changes in the Circumference

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

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