GMAT Prep(Square Inscribed) Pract2

Hi dferm,

To solve this question, remember the rule for 45/45/90 degree triangles: the hypothenuse of these triangles are always 'a*sqrt2', assuming the other two sides are 'a'.

First, from the question, we know that each of the sides of the square S is 6 (perimeter is 24, 24/4 = 6). To get the diameter of the circle T, we need to find the hypothenuse of the triangles (i.e., the diagonal of the square) that we get when we cut the square in half, which is 6*sqrt2, according to our handy formula above. The radius is then 3*sqrt2.

Finally, the circumference of the circle is 2*pi*r, and this comes out to 6*sqrt2*pi.

Hope this helps!

Can someone offer a better explanation...

Thanks...

Hi dferm,

It might help if you draw a picture and start filling in what I wrote above. I know it's a little weird that I'm telling you to work with triangles when the problem gives you a circle and a square. But, if you draw a picture, you'll see that when you cut the square in half diagonally you get two triangles, the hypotenuses of which are the diameter of the circle.

Does this clear it up?

side of square=24/4=6

diagonal= 6*sqrt2 (as it is 45,90,45 triangle)

so, dia of circle=6*sqrt2

perimeter= pie*dia= 6*sqrt2*pie

I wanted to make sure I understand this the diagonal of the square is equal to the circles radius right/ Then d(pi) is equal to the circumference of the circle.
Before I under the impression that 2*pi*r = circumference. :roll:

vladmire wrote:I wanted to make sure I understand this the diagonal of the square is equal to the circles radius right/ Then d(pi) is equal to the circumference of the circle.
Before I under the impression that 2*pi*r = circumference. :roll:

Why the eyeroll? Draw a picture. The diagonal of the square is equal to the diameter of the circle. 2r = d. Therefore C = 2rπ = dπ.

:roll:

Guys,

I clearly understand the explanation above. But what is the reason to equate diagnoal of the square to the diameter of the circle?

Vidhya

Draw a figure to see the relation...

The diagonal of the square = Diameter of the circle..

You could also do it using 45-45-90 triangles.

vidhya16 wrote:Guys,

I clearly understand the explanation above. But what is the reason to equate diagnoal of the square to the diameter of the circle?

Vidhya

Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T?
A. 6π
B. 12π
C. 3√2π
D. 6√2π
E. 12√2π

vidhya16 wrote:Guys,

I clearly understand the explanation above. But what is the reason to equate diagnoal of the square to the diameter of the circle?

Vidhya

Draw the figure:

An inscribed angle is formed by 2 chords.
Angle BAD is an inscribed angle.
Since ABCD is a square, angle BAD = 90.
An inscribed angle of 90 degrees intercepts the DIAMETER of the circle.
For this reason, when a square is inscribed in a circle, the DIAGONAL of the square is also the DIAMETER of the circle.

The diagonal of a square forms a 45-45-90 triangle.
In a 45-45-90 triangle, the sides are proportioned s:s:s√2.
Since the perimeter of the square = 24, s=6, implying that BD = 6√2.
Thus, the circumference of the circle = πd = 6√2π.

The correct answer is D.