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Joined: 16 Apr 2020
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The figure above shows 2 circles. The larger circle has center A
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04 Aug 2021, 04:41
04 Aug 2021, 04:41
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Question Stats:
54% (03:27) correct
45% (02:50) wrong based on 33 sessions
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Two circles.png [ 28.46 KiB | Viewed 3183 times ]
The figure above shows 2 circles. The larger circle has center A, radius R cm, and is inscribed in a square. The smaller circle has center C, radius r cm, and is tangent to the larger circle at point B and to the square at points D and F. Also, points A, B, C, and E are collinear.
Quantity A |
Quantity B |
R |
4r |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
The figure above shows 2 circles. The larger circle has center A
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05 Aug 2021, 00:15
05 Aug 2021, 00:15
3
Explanation:
(Refer to the figure below)
Since, AM = ME = \(R\)
AME is an isosceles right triangle i.e. AE = \(\sqrt{2}R\)
Also, CD = DE = \(r\)
CDE is an isosceles right triangle i.e. CE = \(\sqrt{2}r\)
AE = \(R + r + \sqrt{2}r\)
\(\sqrt{2}R = R + r + \sqrt{2}r\)
\((\sqrt{2}-1)R = (\sqrt{2}+1)r\)
Col. A: \(R\)
Col. B: \(4r\)
Dividing both sides with \(r\);
Col. A: \(\frac{R}{r}\)
Col. B: 4
Col. A: \(\frac{(\sqrt{2}+1)}{(\sqrt{2}-1)}\)
Col. B: 4
Col. A: 5.83
Col. B: 4
Hence, option A
(Refer to the figure below)
Since, AM = ME = \(R\)
AME is an isosceles right triangle i.e. AE = \(\sqrt{2}R\)
Also, CD = DE = \(r\)
CDE is an isosceles right triangle i.e. CE = \(\sqrt{2}r\)
AE = \(R + r + \sqrt{2}r\)
\(\sqrt{2}R = R + r + \sqrt{2}r\)
\((\sqrt{2}-1)R = (\sqrt{2}+1)r\)
Col. A: \(R\)
Col. B: \(4r\)
Dividing both sides with \(r\);
Col. A: \(\frac{R}{r}\)
Col. B: 4
Col. A: \(\frac{(\sqrt{2}+1)}{(\sqrt{2}-1)}\)
Col. B: 4
Col. A: 5.83
Col. B: 4
Hence, option A
Attachments
Two circles.png [ 28.26 KiB | Viewed 2978 times ]
General Discussion
Re: The figure above shows 2 circles. The larger circle has center A
[#permalink]
04 Aug 2021, 05:13
04 Aug 2021, 05:13
hm, cannot figure this one out
