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If B and D are centers of the circles shown in the figure above, and

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Bunuel
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If B and D are centers of the circles shown in the figure above, and [#permalink] New post   21 Nov 2017, 23:11
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If B and D are centers of the circles shown in the figure above, and if BD = 12, BC = 2 and DE = 3, then AB =

(A) 12
(B) 14
(C) 21
(D) 22
(E) 24

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E
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Luckisnoexcuse
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Re: If B and D are centers of the circles shown in the figure above, and [#permalink] New post   21 Nov 2017, 23:55
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Bunuel wrote:

If B and D are centers of the circles shown in the figure above, and if BD = 12, BC = 2 and DE = 3, then AB =

(A) 12
(B) 14
(C) 21
(D) 22
(E) 24

Show Spoiler
Attachment:
2017-11-21_1032.png


Let AB = x..Consider two triangles
A and a Diameter passing through B
A and a Diameter passing through D

We know Diameter of smaller circle = 4 and Diameter of larger circle = 6
Hence
\(AB/AD = 4/6\)
\(x/x+12 = 4/6\)
x= 24
E
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If B and D are centers of the circles shown in the figure above, and [#permalink] New post   22 Nov 2017, 01:18
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Answer is E as follows.

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We have to use properties of similar triangle here.

Triangle ACB is similar to AED
\(\frac{AD}{AB} = \frac{DE}{BC}\) => \(\frac{x+12}{x} = \frac{3}{2}\) => 2x+24 = 3x => x=24

Hence E is the answer
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Re: If B and D are centers of the circles shown in the figure above, and [#permalink] New post   24 Jul 2018, 06:20
The problem can be solved using the similar triangle theorem.
where Triangle ABC and Triangle ADE are similar
Thus BC/DE=AB/AD
2/3=AB/(AB+BD)
Hence we get AB=24 by solving the above equation.
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Re: If B and D are centers of the circles shown in the figure above, and [#permalink] New post   24 Jan 2021, 17:50
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Re: If B and D are centers of the circles shown in the figure above, and [#permalink]
24 Jan 2021, 17:50
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