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# What is the radius of the circle shown above?

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Math Expert
Joined: 02 Sep 2009
Posts: 50619

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11 Sep 2018, 23:21
00:00

Difficulty:

25% (medium)

Question Stats:

88% (01:00) correct 12% (01:15) wrong based on 17 sessions

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What is the radius of the circle shown above?

(1) The length of QR is 5.
(2) The length of PQ is $$\sqrt{75}$$

Attachment:

image014.jpg [ 5.27 KiB | Viewed 290 times ]

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Joined: 29 Aug 2018
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12 Sep 2018, 18:51
1)Triangle QOR is equilateral so r=5
2)Sides will in the ratio r:r:r*root(3)
r=5
So D will be the answer.
Status: Preparing for GMAT
Joined: 25 Nov 2015
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Location: India
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12 Sep 2018, 19:29
1
Bunuel wrote:

What is the radius of the circle shown above?

(1) The length of QR is 5.
(2) The length of PQ is $$\sqrt{75}$$

Attachment:
image014.jpg

S1 - QR=5
$$\angle$$ QOR=180-12=60
$$\angle$$ OQR= $$\angle$$ORQ=60
Sufficient

S2 - PQ=$$\sqrt{75}$$
OP=OQ (radius), $$\angle$$OPQ=$$\angle$$OQP=30, $$\angle$$ POQ=120
PQR is a 30-60-90 triangle, we can find the radius.
Sufficient.

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Re: What is the radius of the circle shown above? &nbs [#permalink] 12 Sep 2018, 19:29
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