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16 Jun 2020, 11:27
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B
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Difficulty:
95%
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37% (02:31) correct
63%
(02:32)
wrong
based on 62
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In the diagram above, the radius of a blue circle is 9 and the radius of a green circle is 4. The line is tangent to all three circles, and the three circles touch each other. What is the radius of the white circle?
A. 2
B. 36/25
C. 6/5
D. 1
E. 5/6
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Attachment:
2020-06-16_2220.png
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firas92
Current Student
Joined: 16 Jan 2019
Last visit: 24 Jul 2026
Posts: 616
Given Kudos: 142
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
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16 Jun 2020, 12:54
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From Triangle ACE,
\(AE=9-4=5, AC=9+4=13\)
So we have a 5-12-13 right triangle which means \(EC=BD=12\)
From right triangles \(AOF\) and \(COG\),
\(\sqrt{(9+r)^2-(9-r)^2}+\sqrt{(4+r)^2-(4-r)^2}=12\)
\(6\sqrt{r}+4\sqrt{r}=12\) or \(10\sqrt{r}=12\)
So \(r=\frac{144}{100}=\frac{36}{25}\)
Answer is (B)
\(AE=9-4=5, AC=9+4=13\)
So we have a 5-12-13 right triangle which means \(EC=BD=12\)
From right triangles \(AOF\) and \(COG\),
\(\sqrt{(9+r)^2-(9-r)^2}+\sqrt{(4+r)^2-(4-r)^2}=12\)
\(6\sqrt{r}+4\sqrt{r}=12\) or \(10\sqrt{r}=12\)
So \(r=\frac{144}{100}=\frac{36}{25}\)
Answer is (B)
Attachments
2020-06-16_2220.png [ 53.72 KiB | Viewed 2868 times ]
