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Sub 505 (Easy)|   Geometry|      
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Bunuel
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The figure above shows three tangent circles (they touch at exactly on 06 Jan 2015, 08:10
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Tough and Tricky questions: Geometry.




The figure above shows three tangent circles (they touch at exactly one point), each with their centers along the same horizontal axis. The biggest circle contains two smaller ones. Of the two smaller circles, the larger one has a radius of 6 inches and the smaller one has a radius of 3 inches. What is the radius of the largest circle (in inches)?

A. 3
B. 6
C. 9
D. 12
E. 18

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Official Answer
C
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The figure above shows three tangent circles (they touch at exactly on 06 Jan 2015, 09:33
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Bunuel

Tough and Tricky questions: Geometry.




The figure above shows three tangent circles (they touch at exactly one point), each with their centers along the same horizontal axis. The biggest circle contains two smaller ones. Of the two smaller circles, the larger one has a radius of 6 inches and the smaller one has a radius of 3 inches. What is the radius of the largest circle (in inches)?

A. 3
B. 6
C. 9
D. 12
E. 18

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say

Largest circle L
Largest of Smaller circle S1
Smallest of Smaller circle S2

Radius of S1 = 6; Diameter SD1 = 12
Radius of S2 = 3; Diameter SD2 = 6
diameter of L = SD1 + SD2 since the centers are in same line
LD1 = 18
LR1 = 9

Ans C
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The figure above shows three tangent circles (they touch at exactly on 07 Jan 2015, 00:33
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Answer = C = 9

Diameter of small circle = 6

Diameter of medium circle = 12

Diameter of large circle = 12+6 = 18

Radius of large circle = 9
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The figure above shows three tangent circles (they touch at exactly on 09 Jan 2015, 07:11
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Bunuel

Tough and Tricky questions: Geometry.




The figure above shows three tangent circles (they touch at exactly one point), each with their centers along the same horizontal axis. The biggest circle contains two smaller ones. Of the two smaller circles, the larger one has a radius of 6 inches and the smaller one has a radius of 3 inches. What is the radius of the largest circle (in inches)?

A. 3
B. 6
C. 9
D. 12
E. 18

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OFFICIAL SOLUTION:

(C) Tangent circles are circles that touch each other, but do not overlap, nor do they leave any gaps between them. If the larger circle has a radius of 6 and the small one a radius of 3, we can calculate the diameter of each as 12 and 6. The diameter of the largest circle, then, would be 18. To find the radius, divide the diameter by 2: 18 / 2 = 9.

The answer is (C).
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The figure above shows three tangent circles (they touch at exactly on 17 Nov 2019, 20:38
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Bunuel

Tough and Tricky questions: Geometry.




The figure above shows three tangent circles (they touch at exactly one point), each with their centers along the same horizontal axis. The biggest circle contains two smaller ones. Of the two smaller circles, the larger one has a radius of 6 inches and the smaller one has a radius of 3 inches. What is the radius of the largest circle (in inches)?

A. 3
B. 6
C. 9
D. 12
E. 18

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The diameter of the large circle is 12 and of the small circle is 6. Thus, the diameter of the largest circle is 18, so the radius is 9.

Answer: C
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