Results 1 to 4 of 4

Math Help - circumscribe a square about a semicircle

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    2

    circumscribe a square about a semicircle

    how do you circumscribe a square about a semicircle with a given radius?
    thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,804
    Thanks
    115
    Quote Originally Posted by Pabo258 View Post
    how do you circumscribe a square about a semicircle with a given radius?
    thanks.
    I've attached a sketch.

    The order of steps is:

    1. black: semicircle and perpendicular bisector

    2. blue: angle bisector

    3. green: tangents to the semicircle

    4. red: perpendicular lines through the endpoints of the diameter to the tangents of the semicircle.
    Attached Thumbnails Attached Thumbnails circumscribe a square about a semicircle-halbkreis_inquad.png  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121
    Cute! I notice that actually touches the semi-circle at two points. In what sense does that "circumscribe" the semi-circle better than, say, the square that would circumscribe the entire circle, which touches the semi-circle at three points?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,804
    Thanks
    115
    Quote Originally Posted by HallsofIvy View Post
    Cute! I notice that actually touches the semi-circle at two points. In what sense does that "circumscribe" the semi-circle better than, say, the square that would circumscribe the entire circle, which touches the semi-circle at three points?
    That depends on how you define "circumscribe".
    As I understand it the semicircle has to determine a square. If the base line of the semicircle (the diameter of the circle) is parallel to one of the square's side then a square isn't necessary. You can take a rectangle too.

    If the base line is tilted less than 45 then the semicircle defines a rectangle too, but the question asks for a square.
    Attached Thumbnails Attached Thumbnails circumscribe a square about a semicircle-halbjreis_inquadfalsch.png  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Semicircle and isosceles problem
    Posted in the Geometry Forum
    Replies: 2
    Last Post: March 11th 2010, 01:49 PM
  2. Inscribe a semicircle into a square
    Posted in the Geometry Forum
    Replies: 4
    Last Post: February 21st 2010, 08:23 PM
  3. inscribe square into semicircle?
    Posted in the Geometry Forum
    Replies: 6
    Last Post: January 17th 2010, 02:20 AM
  4. rectangle and semicircle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 23rd 2009, 10:40 PM
  5. Rectangle Within Semicircle
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 13th 2007, 09:56 PM

Search Tags


/mathhelpforum @mathhelpforum