Results 1 to 5 of 5

Math Help - Circle Cordinate-Geomerty question, intersecting circles?

  1. #1
    LHS
    LHS is offline
    Member
    Joined
    Feb 2009
    From
    Oxford
    Posts
    84

    Exclamation Circle Cordinate-Geomerty question, intersecting circles?

    Any chance I could get a little help with the second part of this question, I've included my working for the first part in case I've messed it up.
    Many thanks to anyone who can help me with this in advance!

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by LHS View Post
    Any chance I could get a little help with the second part of this question, I've included my working for the first part in case I've messed it up.
    Many thanks to anyone who can help me with this in advance!
    Your calculations are OK.

    You have two centers: C_1(3, -4) and C_2(15, 12) and the radii of the two circles are equal: r_1 = r_2 = 10


    Since |\overline{C_1C_2}| = 20 = 2r the circles are tangent to each other. The tangent point is the midpoint of |\overline{C_1C_2}| .

    Therefore T(9, 4)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    LHS
    LHS is offline
    Member
    Joined
    Feb 2009
    From
    Oxford
    Posts
    84
    Thank you! That is very helpful. I thought it may have been something like that, as it said "the point where they touch"
    For future reference is there anyway you can work out where 2 circles intersect like you would would say a circle and a line, but substitution?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by LHS View Post
    Thank you! That is very helpful. I thought it may have been something like that, as it said "the point where they touch"
    For future reference is there anyway you can work out where 2 circles intersect like you would would say a circle and a line, but substitution?
    Let c_1: (x-x_C)^2+(y-y_C)^2 = r^2 denote the first circle and c_2: (x-x_M)^2+(y-y_M)^2=R^2 the second circle.

    Expand the brackets and subtract the first equation from the second columnwise:

    x^2-2x_Cx+x_C^2+y^2-2y_Cy +y_C^2 = r^2

    x^2-2x_Mx+x_M^2+y^2-2y_My +y_M^2 = R^2
    -------------------------------------------------------------------------------
    (2x_C-2x_M)x +(2y_C-2y_M)y=R^2-r^2

    The last line is the equation of the line passing through the points of intersection. That means the problem is reduced to the calculation of points of intersection between a circle and a line.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    LHS
    LHS is offline
    Member
    Joined
    Feb 2009
    From
    Oxford
    Posts
    84
    Ah I see, thank you, I can see that being helpful in future questions
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Non intersecting circles...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 29th 2011, 12:23 PM
  2. Intersecting Circles
    Posted in the Geometry Forum
    Replies: 2
    Last Post: March 26th 2011, 11:16 PM
  3. Two circles intersecting each other...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 25th 2010, 10:32 AM
  4. intersecting circles
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: March 14th 2009, 12:22 AM
  5. Two intersecting circles, Circle 2's...
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 16th 2008, 04:19 AM

Search Tags


/mathhelpforum @mathhelpforum