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      Question

      The circle whose centre is (–3, 2) and which cuts off

      a chord of length 6 on the line 2x–5y+18=0 has radius:
      A √(200/29) Correct Answer Incorrect Answer
      B √(265/29) Correct Answer Incorrect Answer
      C √(297/29) Correct Answer Incorrect Answer
      D √(238/29) Correct Answer Incorrect Answer

      Solution

      We are given:

      • The center of the circle: C(–3, 2)
      • A chord of length 6 lies on the line: 2x – 5y + 18 = 0
      • The circle intersects this line, forming a chord of length 6.
      • We are to find the radius of the circle.
      Geometry Overview We know that if a chord of length L is cut off from a line at distance d from the center of the circle, and the circle has radius R, then:

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