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Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3, 2) and parallel to the coordinate axes touch it. Then the shortest distance of the circle C from the point (5, 5) is :
Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3, 2) and parallel to the coordinate axes touch it. Then the shortest distance of the circle C from the point (5, 5) is :
Updated On: Nov 21, 2024
- \(2\sqrt2\)
- 5
- \(4\sqrt2\)
- 4
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The Correct Option is D
Solution and Explanation
Coordinates of the centre will be: \[ (2, 1) \]
Equation of circle: \[ (x - 2)^2 + (y - 1)^2 = 1 \]
\[ QC = \sqrt{(5 - 2)^2 + (5 - 1)^2} = 5 \]
Shortest distance: \[ RQ = CQ - CR = 5 - 1 = 4 \]
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