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16 Jun 2020, 11:27
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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
Are You Up For the Challenge: 700 Level Questions
Attachment:
2020-06-16_2220.png
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firas92
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Joined: 16 Jan 2019
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Concentration: General Management
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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)
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2020-06-16_2220.png [ 53.72 KiB | Viewed 2642 times ]
