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A circle is a perfectly symmetrical shape where every point on its boundary is equidistant from a fixed center. The equation that represents a circle in a coordinate plane is derived from one of the most fundamental principles in mathematics—the Pythagorean theorem. If a circle is centered at the point (a, b) with a radius r, then every point (x, y) on the circle satisfies the equation (x − a)² (y − b)² = r². This formula arises from the idea that the distance between any point on the circle and
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