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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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