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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # There are two squares in a semi-circle as above figure, OC=CE. If the  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 There are two squares in a semi-circle as above figure, OC=CE. If the [#permalink] ### Show Tags 25 May 2016, 17:30 00:00 Difficulty: 35% (medium) Question Stats: 81% (02:22) correct 19% (04:33) wrong based on 64 sessions ### HideShow timer Statistics 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 *An answer will be posted in 2 days. Attachments 1.png [ 25.26 KiB | Viewed 1243 times ] _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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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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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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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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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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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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