For the line 3x + 2y = 12 and the circle $x^{2} + y^{2} - 4 x - 6 y + 3 = 0,$ which of the following statements is true

Line is a tangent to the circle

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Line is a chord of the circle

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Line is a diameter of the circle

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None of these

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Solution

The correct option is C Line is a diameter of the circle
Centre of the circle is(2, 3). Obviously the line 3x + 2y = 12 passes through the centre of the circle. Hence it is a diameter of the circle.

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