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This resource contains eight problems requiring students to explore the equations of a variety of circles. Many of the problems are open-ended in so much as there is not a specific answer. These problems present the opportunity for rich discussion as students attempt to justify their solution. Students are required to explain whether points lie inside or outside a given circle and whether two points are the two ends of the diameter to a given circle. Students are required to complete the square in order to manipulate the equation of a circle.

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