+537 A quarter-circle is drawn inside a square, as shown below. A point on the quarter-circle has distances of 1 and 8 from two sides of the square.
Find the side length of the square.
https://latex.artofproblemsolving.com/miscpdf/tledzvvo.pdf?t=1574736375974
Sorry I forgot the picture
Set the side lengths equal to x.
That means that the small rectangle has a width 1/x, and a length of 8/x.
The area of the rectangle in terms of x is therefore: 1/x * 8/x = 8/x2
And you can calculate the area of the rectangle as 1 * 8 = 8.
So you have the equation of 8 = 8/x2
I will leave you to solve that, it should take less than 30 seconds.
This is CalcUser not logged in, thanksgiving break has granted me a little more time on this website.
+128474 Let the radius of the circle and the side of the square = R
If we let the bottom right of the square = (0, 0) then we can find P as ( -R + 8, R - 1)
So.....we have that
(-R + 8)^2 + (R - 1)^2 = R^2 simplify
R^2 - 16R + 64 +R^2 - 2R + 1 = R^2
R^2 - 18R + 65 = 0 factor
(R - 13) ( R - 5) = 0
Since R must be greater than 8.......the radius must be 13 = side of the square
Here's a pic :
