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 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

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