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JEE MainMathematicsCircle

A circle passes through the vertices of a triangle formed by the lines L₁: 2x + 3y = 72 , L₂: 3x - 2y = 30 , and L₃: 12x + 5y = 120 . If a point D(k,k) , where k > 0 , lies on this circle, then the value of k is

Options

  1. A7
  2. B12
  3. C17
  4. D15

Correct answer

C. 17

Step-by-step solution

The slope of line L₁ is - 2 3 and the slope of line L₂ is 3 2 . Since the product of their slopes is (- 2 3 ) ( 3 2 ) = -1 , the lines L₁ and L₂ are perpendicular. Thus, the triangle formed by these three lines is a right-angled triangle, with the right angle at the intersection of L₁ and L₂ . The circumcircle of a right-angled triangle has its hypotenuse as the diameter. The hypotenuse lies on the third line, L₃ . The endpoints of the diameter are the intersections of L₃ with L₁ and L₃ with L₂ . Intersection of L₁

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