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maths c2 solomon paper E hardest question ever faced!!!!!

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1. hi guys; i CANNOT GET MY HEAD ROUND THIS UGLY QUESTION !!! so question is: The circle C has the equation
x^2 + y^2 +10x - 8y +k =0,
where k is a constant.
Given that the point with coordinates (−6, 5) lies on C,
(a) find the value of k, (2)
(b) find the coordinates of the centre and the radius of C. (3)
A straight line which passes through the point A (2, 3) is a tangent to C at the point B.
(c) Find the length AB in the form k 3 .

part A B is fine for me but part c is driving me insane! pls pls pls help !!
2. Draw a triangle ABX where X is the centre. You know the length of XB, you can work out the length of AX. And this should allow you to find AB
3. Draw a diagram, you should notice that it forms a right angle triangle with one side being the radius, the other being AB and the other being A-center, you can find the length of A-center and you know the radius, do some pythagoras and there you go ;p
4. Yeah, find the length between the centre and A (because you know both of these co-ordinates), and the length between the centre and point B, which is just the radius, then you have yourself a right angled triangle with AB as the missing side so you can just use Pythagoras
5. thank you !!
6. I can't do part c) ? Anyone

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7. Bump

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8. As already stated, draw a diagram and you should end up with a right angled triangle, then use pythagoras to solve for the unknown side
9. I have drawn but I can't find it

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10. radius is root 2 so use pythagoras
11. (Original post by Kawaii289)
radius is root 2 so use pythagoras
Thank you, I didn't realise

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12. no problem
13. (Original post by Fish40)
Thank you, I didn't realise

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remember circle theorems is in the specification so remember those "laws".
14. Can someone leave the answers of all the parts? ; a) b) and c) ?? PLEASE!

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