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M22-25

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M22-25 [#permalink]

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New post 16 Sep 2014, 01:17
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If a circle is inscribed in a square, what is the ratio of the diagonal of the square to the radius of the circle?

A. \(\frac{1}{2}\)
B. \(\frac{1}{\sqrt{2}}\)
C. \(\sqrt{2}\)
D. 2
E. \(2\sqrt{2}\)
[Reveal] Spoiler: OA

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Re M22-25 [#permalink]

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New post 16 Sep 2014, 01:17
Official Solution:

If a circle is inscribed in a square, what is the ratio of the diagonal of the square to the radius of the circle?

A. \(\frac{1}{2}\)
B. \(\frac{1}{\sqrt{2}}\)
C. \(\sqrt{2}\)
D. 2
E. \(2\sqrt{2}\)

If \(x\) is the side of the square, then the diagonal of the square is \(\sqrt{2}x\) and the radius of the circle is \(\frac{x}{2}\). The required ratio \(= \frac{\sqrt{2}x}{\frac{x}{2}} = 2\sqrt{2}\).

Answer: E
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M22-25 [#permalink]

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New post 17 Mar 2017, 12:00
I didn't get it :(
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M22-25 [#permalink]

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New post 18 Dec 2017, 10:08
Bunuel niks18

Quote:
If \(x\) is the side of the square, then the diagonal of the square is \(\sqrt{2}x\)

This is simple application of Pythagoras theorem


Quote:
and the radius of the circle is \(\frac{x}{2}\). The required ratio \(= \frac{\sqrt{2}x}{\frac{x}{2}} = 2\sqrt{2}\).

Is this from the property that side of square = diameter for circle inscribed in triangle?
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Expert Post
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M22-25 [#permalink]

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New post 18 Dec 2017, 10:15
adkikani wrote:
Bunuel niks18

Quote:
If \(x\) is the side of the square, then the diagonal of the square is \(\sqrt{2}x\)

This is simple application of Pythagoras theorem


Quote:
and the radius of the circle is \(\frac{x}{2}\). The required ratio \(= \frac{\sqrt{2}x}{\frac{x}{2}} = 2\sqrt{2}\).

Is this from the property that side of square = diameter for circle inscribed in triangle?


The diagonal of the square is: \(diagonal^2=side^2+side^2=x^2 + x^2\) --> \(diagonal=\sqrt{2}x\)

When a circle is inscribed in a square, the side of a square = the diameter of the circle, so the radius of the circle is \(\frac{side}{2}\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: M22-25 [#permalink]

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New post 26 Jan 2018, 08:40
+1 for option E
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Re: M22-25   [#permalink] 26 Jan 2018, 08:40
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