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THA 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 its center must always be exactly r. By considering this distance as the hypotenuse of a right triangle, where the horizontal and vertical differences between the center and the point on the circle form the two legs, we apply the Pythagorean theorem to derive the equation. This simple yet powerful formula allows us to describe circles algebraically and analyze their properties in a Cartesian coordinate system.
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