Diagonal length (Posted on 2002-06-02)

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 12/SQRT(5) The main diagonal of a square is SQRT(2) * length of the square's side, so DB is 12*SQRT(2)/SQRT(5) = 7.59

	Subject	Author	Date
	answer	K Sengupta	2007-05-15 04:21:53
	re: Solution	prashant	2004-03-26 07:02:04
	Solution	Antonio	2003-08-22 03:11:55
	re: What am I doing wrong?	Nick Reed	2002-12-06 14:29:48
	What am I doing wrong?	Jimmy Bob	2002-12-06 13:25:33
	whoops!	James	2002-10-24 11:44:47
	this isnt trig just geometry!	James	2002-10-24 11:21:34
	No Trig	TomM	2002-06-02 11:35:13