Results 1 to 5 of 5

Math Help - Are inscribable quadrilaterals always circumscribable???

  1. #1
    Member aldrincabrera's Avatar
    Joined
    Jun 2011
    From
    Dumaguete City
    Posts
    90

    Are inscribable quadrilaterals always circumscribable???

    ,.,.good day,.,i was proving "are circumscribable quadrilaterals always inscribable" and i found out that it is not,.,it only happens for some conditions,.,.but my teacher ask me the other way around,.,now i am having a hard time proving "are inscribable quadrilaterals always circumscribable" can anyone please help me with the proof???thnx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,711
    Thanks
    630

    Re: Are inscribable quadrilaterals always circumscribable???

    Hello, aldrincabrera!

    i was proving "Are circumscribable quadrilaterals always inscribable?"
    and i found out that they are not ... it only happens for certain conditions.

    But my teacher ask me the other way around. .Now i am having a hard time
    proving "Are inscribable quadrilaterals always circumscribable?"
    Can anyone please help me with the proof?

    The answer to both questions is "No."
    No proof is required . . . just a counterexample.


    I assume a "circumscribable quadriateral" is one which can be circumscribed.
    . . That is, it can be inscribed in a circle.

    Code:
                  * * *
            A o-----------o B
            */             \*
           */               \*
           /                 \
        D o-------------------o C
          *                   *
          *                   *
    
           *                 *
            *               *
              *           *
                  * * *
    Quadrilateral ABCD is circumscribable.
    But no circle can be inscribed within it.



    Code:
                A o---*-*-*---------------o B
                 /*           *          /
                *                *      /
               *                 *     /
              /                       / 
             /*                   *  /
            / *                   * /
           /  *                   */
          /                       /
         /     *                 *
        /       *               *
       /          *           */
    D o---------------*-*-*---o C
    Quadrilateral ABCD is inscribable.
    But no circle can be circumscribed around it.
    . . (In this case it is, after all, a rhombus.)


    In fact, the only quadrilateral which is inscribable
    . . and circumscribable is a square.

    Last edited by Soroban; June 16th 2011 at 11:01 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123

    Re: Are inscribable quadrilaterals always circumscribable???

    Quote Originally Posted by Soroban View Post
    ...

    In fact, the only quadrilateral which is inscribable
    . . and circumscribable is a square.

    [/size]
    Well, ääh, not quite. See attachment.
    Attached Thumbnails Attached Thumbnails Are inscribable quadrilaterals always circumscribable???-inscribcircumscrib4eck.png  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,711
    Thanks
    630

    Re: Are inscribable quadrilaterals always circumscribable???

    Hello, earboth!

    You're right, of course.

    Silly me . . . I had that in my list of sketches, too.

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member aldrincabrera's Avatar
    Joined
    Jun 2011
    From
    Dumaguete City
    Posts
    90

    Re: Are inscribable quadrilaterals always circumscribable???

    ,.,as i was solving "are circumscribable quadrilaterals always inscribable" i found out this certain condition that a circumscribable quadrilateral is inscribable if its area equals the square root of the product of its four sides,.now, i am having a hard tym proving "are inscrabable...". ur sketches were really helpful but it showed me that there is a number of quadrilateral that are inscribable and circumscribable at the same time,.,.can u help me find those conditions???thnx a lot
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Diagonals of a Circumscribable Quadrilateral
    Posted in the Geometry Forum
    Replies: 3
    Last Post: July 27th 2011, 05:38 PM
  2. Replies: 6
    Last Post: July 7th 2011, 12:12 PM
  3. Replies: 6
    Last Post: June 20th 2011, 03:48 AM
  4. Quadrilaterals
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 18th 2010, 06:07 PM
  5. Replies: 16
    Last Post: August 18th 2010, 02:45 AM

Search Tags


/mathhelpforum @mathhelpforum