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Math Expert V
Joined: 02 Sep 2009
Posts: 53801
In the figure above, line segment AD is the diameter of circle O, line  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 47% (03:14) correct 53% (03:06) wrong based on 55 sessions

### HideShow timer Statistics In the figure above, line segment AD is the diameter of circle O, line segment AO is the diameter of circle B, line segment OD is the diameter of circle C, and circle E is tangent to each of the other circles. If the radius of circle O is 4, what is the radius of circle E?

A. 2/3

B. 3/4

C. 1

D. 4/3

E. 3/2

Attachment: FourCircles.png [ 11.47 KiB | Viewed 2169 times ]

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Current Student P
Joined: 02 Jul 2017
Posts: 294
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38 In the figure above, line segment AD is the diameter of circle O, line  [#permalink]

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1
therefore OB=OC=2

Now let radius of circle E =x

BE=EC=2+x

As BE=EC and OB=OC, implies EO is perpendicular to BC

Now in triangle EOB :
OB=2
EB=2+x
EO =4-x (radius of circle O - radius of circle E)

solving Pythagoras : OB^2+OE^2=BE^2
=> x=4/3

Target Test Prep Representative P
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Re: In the figure above, line segment AD is the diameter of circle O, line  [#permalink]

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2
Bunuel wrote: In the figure above, line segment AD is the diameter of circle O, line segment AO is the diameter of circle B, line segment OD is the diameter of circle C, and circle E is tangent to each of the other circles. If the radius of circle O is 4, what is the radius of circle E?

A. 2/3

B. 3/4

C. 1

D. 4/3

E. 3/2

Attachment:
FourCircles.png

Since the radius of circle O is 4 (i.e., AO = 4), BO = 2. We can form a right triangle by connecting B, E, and O. If we let x = radius of circle E, the legs of right triangle BOE are BO = 2 and OE = 4 - x, and its hypotenuse is BE = 2 + x. Now, using the Pythagorean theorem, we have:

2^2 + (4 - x)^2 = (2 + x)^2

4 + 16 - 8x + x^2 = 4 + 4x + x^2

16 - 8x = 4x

16 = 12x

x = 16/12 = 4/3

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Re: In the figure above, line segment AD is the diameter of circle O, line  [#permalink]

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_________________ Re: In the figure above, line segment AD is the diameter of circle O, line   [#permalink] 20 Feb 2019, 00:17
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# In the figure above, line segment AD is the diameter of circle O, line

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