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    How to do part iv)
    A circle has equation (x − 3)
    2 + (y + 2)
    2 = 25.
    (i) State the coordinates of the centre of this circle and its radius. [2]
    (ii) Verify that the point A with coordinates (6, −6) lies on this circle. Show also that the point B on
    the circle for which AB is a diameter has coordinates (0, 2). [3]
    (iii) Find the equation of the tangent to the circle at A. [4]
    (iv) A second circle touches the original circle at A. Its radius is 10 and its centre is at C, where BAC
    is a straight line. Find the coordinates of C and hence write down the equation of this second
    circle.
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    BAC is a straight line and AC=10. Assume it is at (p,q). The distance between (3, -2) and (p,q) is 15.
    Also, since C lies on the line AB (whose equation is easy to work out), you can get another equation in (p,q).

    Without doing the question, I can't see why there are not two possible circles touching A but hopefully the above helps.
 
 
 
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