Question:
A circle passes through the points \( (1, 1) \) and \( (2, -1) \), and its center lies on the line \( x + y = 4 \). What is the radius of the circle?
A circle passes through the points \( (1, 1) \) and \( (2, -1) \), and its center lies on the line \( x + y = 4 \). What is the radius of the circle?
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The center of the circle lies on the perpendicular bisector of the line joining the two given points.
Updated On: Jan 22, 2025
- \( \sqrt{5} \)
- \( \sqrt{10} \)
- \( \sqrt{13} \)
- \( \sqrt{17} \)
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The Correct Option is A
Solution and Explanation
First, find the center of the circle. The center lies on the line \( x + y = 4 \), and the circle passes through two given points. Use the midpoint formula to find the center by averaging the coordinates of \( (1, 1) \) and \( (2, -1) \), and then use the distance formula to find the radius.
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