Find the relationship between the circumradius of a triangle and the radii of the circles that pass through the triangle’s vertices.
Examine the relationship between two secants that pass through the intersections of two circles.
Given coordinates of the endpoints of a circle’s diameter, find the circle’s area.
Find the equation of a circle based on its radius, center, and locus of points.
Determine a relationship between segments formed by the intersection of two chords of a circle.
Find the triangles with maximum and minimum area if two sides of the triangle are determined by radii of the circle.
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.
Investigate how the location of an angle’s vertex affects its relationship to the measure(s) of the arc(s) it intercepts.
Determine the sector of a circle that will produce a cone with maximum volume.
Explore how changing the diameter of a circle affects its circumference.
Find a relationship between the area of a circle and the areas of the tangent circles along the circle’s diameter.
Construct a circle with five equal regions that do not intersect at the circle’s center.
Compare the area and circumference of a circle inscribed in a region between two intersecting circles.