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Circles (Chord) Help Watch

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    Hi there, im currently revising C1 (OCR) in preparation for the exam in January. Im revising circles at the moment but i am unsure what to do and where to begin with this question:

    The straight line y=20-3x meets the circle at x^2+y^2-2x-14y=0 at the points A and B. Calculate the exact length of the chord AB.

    I know the centre is (1,7) and the gradient of the line is -3 but other than that i dont know what to do next.

    Thanks for any help.
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    Solve the two equations simultaneously, and then use Pythagoras to find the distance between A and B.
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    (Original post by marcusmerehay)
    Solve the two equations simultaneously, and then use Pythagoras to find the distance between A and B.
    What would the result of the simultaneous equation give me? A? B? Midpoint? Both?
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    (Original post by ~Sparked~)
    What would the result of the simultaneous equation give me? A? B? Midpoint? Both?
    Think about it - it will give you the values of x that are contained on both the straight line and the circle.
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    Ok so i now have (6,2) and (2,14). Do i now find the distance between them or have i missed a step out?
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    You haven't missed any steps. Use Pythagoras' Theorem to find the distance between them.
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    (Original post by marcusmerehay)
    You haven't missed any steps. Use Pythagoras' Theorem to find the distance between them.
    When you say pythagoras theroem do you mean the distance formula i.e root (y2-y1) + (x2-x1)and squared format.

    (Sorry i cant be bothered to try and put it into the latex formula. Lol.
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    Essentially, yes.

    The formula is given as r^2 = x^2 + y^2 where x and y are the component-wise distances in the x and y directions.
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    Okidoke, my answer corresponds to that in the back of the textbook. Thanks.
 
 
 
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