Results 1 to 7 of 7

Math Help - Intersection of circle and square

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    121

    Intersection of circle and square

    Consider the system of equations
    x^2 + y^2 = R^2 (circle)
    |x| + |y| = 1 (square)
    I need to find the number of solutions to the two equations for different values of R.
    I know if R>1 there are 0 solutions, 4 if R=1. But there is a value, t, of R for which the circle intersects the square 8 times i.e. t<R<1. My problem is how to find the value t?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    There is actually a range of values t for which the square and the circle will intersect in 8 locations. There is another value of t aside from 1 where the square and the circle intersect in 4 locations. Determine this value, and call it c. What happens for values of t such that c<t<1?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2008
    Posts
    121
    Hi

    Yes, the other point is where c=t....I know the answer for t is sqrt2 / 2 but I can't figure out how to get that value...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    Quote Originally Posted by bigdoggy View Post
    Hi

    Yes, the other point is where c=t....I know the answer for t is sqrt2 / 2 but I can't figure out how to get that value...
    That is the value for which the circle is inscribed in the square. The radius of the circle is the distance from the center of the square to a midpoint of one of the sides of the square.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,793
    Thanks
    1688
    Awards
    1
    Look at the diagram. The circles have radii of 0.8, 1, & 1.2.
    What is the distance from (0,0) to (1,1)?
    Attached Thumbnails Attached Thumbnails Intersection of circle and square-cirs.gif  
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Nov 2008
    Posts
    121
    Quote Originally Posted by Plato View Post
    Look at the diagram. The circles have radii of 0.8, 1, & 1.2.
    What is the distance from (0,0) to (1,1)?
    The distance is sqrt2...
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Nov 2008
    Posts
    121
    Quote Originally Posted by icemanfan View Post
    The radius of the circle is the distance from the center of the square to a midpoint of one of the sides of the square.
    Why is this?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Intersection Points in a Circle
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: December 7th 2009, 09:02 PM
  2. Intersection between circle and line
    Posted in the Geometry Forum
    Replies: 1
    Last Post: August 30th 2009, 01:19 PM
  3. Intersection of line with circle
    Posted in the Geometry Forum
    Replies: 3
    Last Post: April 7th 2009, 02:50 PM
  4. 2 circle intersection
    Posted in the Geometry Forum
    Replies: 2
    Last Post: October 9th 2008, 08:10 PM
  5. Intersection of Circle and Parabola
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 18th 2007, 06:39 AM

Search Tags


/mathhelpforum @mathhelpforum