A Circle Journey

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The initial task involves using factors of 12 and -12 to set up two points. Compasses are used to draw a circle that has the two points as its diameter. An interesting feature of the resulting circle is that the circumference always goes through the origin. A Geogebra file is provided that allows different factors of 12 and -12 to be demonstrated.

The ideas of midpoints, radius, and the equation of a circle are used to prove that the circumference of the circle will always pass through the origin.

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