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Math Expert V
Joined: 02 Sep 2009
Posts: 65187
A square is inscribed in a big circle and a small circle is inscribed  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 74% (01:53) correct 26% (01:09) wrong based on 26 sessions

### HideShow timer Statistics A square is inscribed in a big circle and a small circle is inscribed in the square as shown in the figure above. (All of them are concentric and their center is the point O). If the radius of the big circle is √2 cm, what is the perimeter of the small circle?

A. 1
B. 2
C. 3
D. π
E. 2π

Attachment: 1.png [ 9.72 KiB | Viewed 321 times ]

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Director  P
Joined: 04 Sep 2015
Posts: 643
Location: India
WE: Information Technology (Computer Software)
Re: A square is inscribed in a big circle and a small circle is inscribed  [#permalink]

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Bunuel wrote: A square is inscribed in a big circle and a small circle is inscribed in the square as shown in the figure above. (All of them are concentric and their center is the point O). If the radius of the big circle is √2 cm, what is the perimeter of the small circle?

A. 1
B. 2
C. 3
D. π
E. 2π

Attachment:
1.png

IMO E.

Sol
Radius of outer circle=root2 that means diameter=2root2
the diagonal of the square=2root2 so the side must be 2
the side of the square is equalt to the diameter of teh inner circle so 1
and the permeter=2PiR=2Pi.
Intern  B
Joined: 21 May 2020
Posts: 9
Re: A square is inscribed in a big circle and a small circle is inscribed  [#permalink]

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Diagonal of square = diameter of bigger circle = 2(root 2)
Side of square = 2 [if diagonal is 2(root 2)]
Side of square is diameter of smaller circle = 2
Perimeter of smaller circle is pi(diameter) = 2pi

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GMAT Club Legend  V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4345
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: A square is inscribed in a big circle and a small circle is inscribed  [#permalink]

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Bunuel wrote: A square is inscribed in a big circle and a small circle is inscribed in the square as shown in the figure above. (All of them are concentric and their center is the point O). If the radius of the big circle is √2 cm, what is the perimeter of the small circle?

A. 1
B. 2
C. 3
D. π
E. 2π

Attachment:
1.png

Radius fo Small Circle, r = Side of square = a
Radius fo Big Circle, R = Diagonal of square = a√2

i.e. $$\frac{r}{R} = \frac{a}{a√2}$$

i.e. $$r = (\frac{1}{√2})*√2 = 1$$

$$Circumference = 2πr = 2π$$

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Re: A square is inscribed in a big circle and a small circle is inscribed  [#permalink]

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Bunuel wrote: A square is inscribed in a big circle and a small circle is inscribed in the square as shown in the figure above. (All of them are concentric and their center is the point O). If the radius of the big circle is √2 cm, what is the perimeter of the small circle?

A. 1
B. 2
C. 3
D. π
E. 2π

Attachment:
1.png

Solution

• Let us assume that the side of the square is a.
• Now, Diameter of the big circle = diagonal of the square o $$⟹2* \sqrt{2} = a*\sqrt{2} ⟹ a = 2$$
• Also, side of the square = diameter of the small circle
o Diameter of the small circle $$= a = 2$$
• Thus, the circumference of the small circle $$= \pi* diameter = 2*\pi$$
Thus, the correct answer is Option E.
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Joined: 11 Feb 2019
Posts: 308
Re: A square is inscribed in a big circle and a small circle is inscribed  [#permalink]

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IMO E.

Diameter of the big circle = Diagonal of square

and Side of square = \sqrt{2} Side of square

Using above we can solve this.
Attachments WhatsApp Image 2020-06-02 at 5.18.51 PM.jpeg [ 167.9 KiB | Viewed 172 times ]

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NJ Re: A square is inscribed in a big circle and a small circle is inscribed   [#permalink] 02 Jun 2020, 07:21

# A square is inscribed in a big circle and a small circle is inscribed  