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Geometry and Trigonometry / Circles Difficulty: Hard

The equation $open parenthesis, x plus 6, close parenthesis, squared, plus, open parenthesis, y plus 3, close parenthesis, squared, equals 121$ defines a circle in the xy‑plane. What is the radius of the circle?

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Explanation

The correct answer is 11. A circle with equation $open parenthesis, x minus a, close parenthesis, squared, plus, open parenthesis, y minus b, close parenthesis, squared, equals r squared$ , where a, b, and r are constants, has center $with coordinates a, comma b$ and radius r. Therefore, the radius of the given circle is $the square root of 121$ , or 11.