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# jan2010 c1 mei

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1. 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.
2. 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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