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AP EAMCET2011MathematicsCircle

If the lines 3 x+4 y-14=0 and 6 x+8 y+7=0 are both tangents to a circle, then its radius is

Options

  1. A7
  2. B7 2
  3. C7 4
  4. D7 6

Correct answer

C. 7 4

Step-by-step solution

Given, lines are both tangents to a circle we observe that, both lines are parallel i.e., aligned 3 x+4 y-14 & =0 3 x+4 y+ 7 2 & =0 aligned So, radius of circle = 1 2 (distance between two parallel lines) aligned & = 1 2 |7 / 2+14| 9+16 & = 1 2 35 / 2 5 = 1 2 7 2 & = 7 4 aligned

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