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JEE MainMathematicsCircle

A rectangle is inscribed in a circle. One of its sides lies on the line 3x - 4y + 15 = 0 and a diameter of the circle lies on the line 3x - 4y - 5 = 0 . If the area of the rectangle is 120 , then the length of the diameter of the circle is _____.

Correct answer

17

Step-by-step solution

The distance between the parallel lines 3x - 4y + 15 = 0 and 3x - 4y - 5 = 0 is the perpendicular distance from the center of the circle to the side of the rectangle. Let this distance be d . Then, d = |15 - (-5)| 3^2 + (-4)^2 = 20 5 = 4 . The length of the side of the rectangle adjacent to the given side is twice this distance. Let the width of the rectangle be w . Then, w = 2 4 = 8 . Given that the area of the rectangle is 120 , the length of the other side is l = 120 8 = 15 . The diameter of the circumscribed ci

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