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Diagonal length (Posted on 2002-06-02) Difficulty: 4 of 5
The diameter of the circle (O), (XY) is 12cm.

Two adjacent vertices of the square (ABCD) lie on the diameter of that circle, while the other two vertices lie on the circumference of the circle.

What is the length of a diagonal of this square (DB)?

  Submitted by Dulanjana    
Rating: 3.5833 (12 votes)
Solution: (Hide)
Consider the triangle OBC. It's a right triangle with the hypothenuse equal to the radius of the circle (6cm), and its short leg (OC) is half the length of the long leg (BC).

Let's designate the length of OC as x. then:

   x^2 + (2x)^2 = 36
   5 * x^2 = 36
   x^2 = 36/5
   x = 6/SQRT(5)
The side of the square, being 2*x is then
The main diagonal of a square is SQRT(2) * length of the square's side, so DB is
   12*SQRT(2)/SQRT(5) =

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2007-05-15 04:21:53
re: Solutionprashant2004-03-26 07:02:04
SolutionSolutionAntonio2003-08-22 03:11:55
re: What am I doing wrong?Nick Reed2002-12-06 14:29:48
What am I doing wrong?Jimmy Bob2002-12-06 13:25:33
whoops!James2002-10-24 11:44:47
this isnt trig just geometry!James2002-10-24 11:21:34
SolutionNo TrigTomM2002-06-02 11:35:13
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