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A straight line passing through the point P(3, 11) intersects the circle x² + y² = 9 at the points A and B. The value of PA · PB is
- 9
- 121
- 205
- 139
Correct answer: 121
Solution
The value of PA · PB is determined by the power of point P with respect to the circle, which is calculated as the square of the distance from P to the center of the circle minus the square of the radius. Here, the distance from P(3, 11) to the center (0, 0) is 3² + 11² = 130, and the radius squared is 9, leading to PA · PB = 130 - 9 = 121.
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