riteshgmat wrote:
Bunuel wrote:
In a certain playground, a square sand box rests in a circular plot of grass so that the corners of the sandbox just touch the edge of the plot of grass at points W, X, Y and Z, as shown. What is the distance from point W to point Y?
The distance from W to Y equals to the diameter so to 2r.
(1) The area of the circular plot is 49π --> \(\pi{r^2}=49\pi\) --> \(r=7\). Sufficient.
(2) The ratio of the area of the sand box to the area of the circular plot is 2/π --> the area of a square is \(\frac{diagonal^2}{2}=\frac{4r^2}{2}=2r^2\) and the area of a circle is \(\pi{r^2}\) --> the ratio thus is \(\frac{2}{\pi}\). So, we already knew that ratio from the stem. Not sufficient.
Answer: A.
Hi Bunnel,
I have assume that distance from W to Y will not pass from centre of the circle. So i have chosen E as the answer.
Is their any rule which specifies that when a square is placed inside a circle (as described in the question), the diameter of the circle will be equal to the diagnoal of a square .
The property is that if you draw a triangle inside a circle such that the diameter is one of the sides of the triangle, then the angle made by triangle on the circumference is a right angle (=90 degrees). In other words, a triangle inside a circle such that the diameter is one of the sides of the triangle will be a right angled triangle.
In a square, the diagonal divides it into 2 right triangles and as such any square drawn inside a circle (such that all the 4 points of the square lie on the circle) will have the diagonal as the diameter of the circle.
Hope this helps.