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There are two squares in a semi-circle as above figure, OC=CE. If the

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There are two squares in a semi-circle as above figure, OC=CE. If the  [#permalink]

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New post 25 May 2016, 17:30
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A
B
C
D
E

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There are two squares in a semi-circle as above figure, OC=CE. If the radius of a semi-circle is 4√5, what is the area of the small square?
A. 12
B. 14
C. 15
D. 16
E. 27

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Re: There are two squares in a semi-circle as above figure, OC=CE. If the  [#permalink]

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New post 26 May 2016, 21:27
Let us assume x = OC = OE
Side of larger square = BO + OC = x + x = 2*x or CD = 2*x
Using pythagoras theorem
(2*x)^2 + x^2 = (4*sqrt(5))^2
5*x^2 = 16*5 ==> x = 4
Area of smaller square = x*x = 4*4 = 16
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There are two squares in a semi-circle as above figure, OC=CE. If the  [#permalink]

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New post 26 May 2016, 22:42
Say OC = x. Then BC= 2x. This means that CD = 2x.

Consider \(\triangle\) OCD,

\(OC^2\) + \(DC^2\) = Square of (4* \(\sqrt{5}\))
\(x^2\)+4\(x^2\) = 80

5\(x^2\)=80

\(x^2\) = 16.

We want area of smaller square; which is \(x^2\). So our answer is 16.

D is the correct option.
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Re: There are two squares in a semi-circle as above figure, OC=CE. If the  [#permalink]

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New post 28 May 2016, 18:39
If OC=GC=DG=a, then a^2+(2a)^2=(4√5)^2=80. From 5a^2=80, we get a^2=16. So the area of the small square is a^2=16. Hence, the correct answer is D.
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Re: There are two squares in a semi-circle as above figure, OC=CE. If the  [#permalink]

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New post 26 Nov 2018, 06:06
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Re: There are two squares in a semi-circle as above figure, OC=CE. If the &nbs [#permalink] 26 Nov 2018, 06:06
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