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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Tangent Along the Diameter

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

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Equal Areas

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

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Tangential Circles

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

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Medians of a Triangle

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Determine the relationship between the coordinates of the vertices of a triangle and its centroid.

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Equation of a Circle

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Find the equation of a circle based on its radius and locus of coordinates.

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The Slope of a Curve

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Explore the variability of the slope of a curve on small intervals.

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