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Math Help - Circle

  1. #1
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    Circle

    Hi

    I have two circle questions that I am a bit unsure of:

    1.

    Show that each of the circles with equations (x-3) +(y-2) = 25 and (x-2) + (y-6) = 25 passes through the centre of the other.

    2.

    The circle with centre Q has equation (x-5) + (y-8) = 9. PQR is a diameter of this circle parallel to the y-axis. The circles with centres P and R touch the circle with centre Q at R and P respectively. Find the equations of the larger circles.

    EDIT:
    Sorry, I've found another I can't do. I've managed to partially solve it, but am unable to complete.

    In this sketch of a road roller, the diameter of the front wheel is half that of the rear wheel. The distance AB is 35 units. The equation of the rear wheel is (x-12) + (y-13) = 100. Find the equation AB and the equation of the front wheel.

    Thank you in advance
    Last edited by HighlyFlammable; May 3rd 2011 at 03:22 PM.
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  2. #2
    Super Member Quacky's Avatar
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    Where is the centre of (x-3)^2+(y-2)^2=25? You don't need to calculate anything for this, just glimpse at the equation. Once you've found the co-ordinates of the centre (which took me roughly 0 seconds), substitute them into (x-2)^2 + (y-6)^2 and show that you get 25. Then do the same for the other circle.

    For 2, similarly, what are the coordinates of Q? So what are the coordinates of P and R? The coordinates of P and R are the centres of the larger circles. You know that the circles intersect at the points R and P (although not both), and from there you should be able to set up something to find the equations of the larger circles.

    What have you been able to do?

    Hint for 1)

    Hint for 2)
    Last edited by Quacky; May 3rd 2011 at 06:17 PM.
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  3. #3
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    Well, I think that the coordinate of A is (12,3) and I got the radius of the smaller circle as 5. I also thought that maybe the x coordinate for B is 23, but I'm always wary of my own working :P
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  4. #4
    Super Member Quacky's Avatar
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    Quote Originally Posted by HighlyFlammable View Post
    Well, I think that the coordinate of A is (12,3) and I got the radius of the smaller circle as 5. I also thought that maybe the x coordinate for B is 23, but I'm always wary of my own working :P
    Without having the sketch referred to in the question, it's difficult to say. The centre is (12,13), as I think you meant. But I don't know what AB represents.
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