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# If the 5 semicircles shown above are identical, what is the diameter

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Joined: 02 Sep 2009
Posts: 65764
If the 5 semicircles shown above are identical, what is the diameter  [#permalink]

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22 Jun 2020, 02:38
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Difficulty:

45% (medium)

Question Stats:

65% (02:08) correct 35% (02:10) wrong based on 52 sessions

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If the 5 semicircles shown above are identical, what is the diameter of one semicircle?

A. 32
B. 33
C. 34
D. 35
E. 36

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Re: If the 5 semicircles shown above are identical, what is the diameter  [#permalink]

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22 Jun 2020, 03:09
2
Line segment = diameter*3 + 12 + 12
Or,
Line segment = diameter*3 + 22 + 16 + 22
=> {Diameter*3 + 24} = { Diameter*2 + 60}
=> Diameter = 36

IMO E

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If the 5 semicircles shown above are identical, what is the diameter  [#permalink]

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22 Jun 2020, 03:19
3
1
Bunuel wrote:
If the 5 semicircles shown above are identical, what is the diameter of one semicircle?

A. 32
B. 33
C. 34
D. 35
E. 36

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Re: If the 5 semicircles shown above are identical, what is the diameter  [#permalink]

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22 Jun 2020, 03:33
1
Bunuel wrote:

Attachment:
2020-06-22_1426.png

This is how I did it.

Diameter = d
for the first semicircle:
the overlapping line is d-22.

for the second semi circle
the second overlapping line is:
d-(d-22 +12)
= 10

for the third semi circle d = 10+16+10 =36

Option E
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Re: If the 5 semicircles shown above are identical, what is the diameter  [#permalink]

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22 Jun 2020, 06:06
2
Bunuel wrote:

If the 5 semicircles shown above are identical, what is the diameter of one semicircle?

A. 32
B. 33
C. 34
D. 35
E. 36

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Attachment:
2020-06-22_1426.png

Move the bottom left semi circle to the left by 22 units so that it coincides with the top left semi circle and move the bottom right semicircle by 22 units so that it coincides with the top right semicircle

Now the distance between the two bottom semi circles is 16+22+22=60

This distance is also equal to 12+Diameter+12 (from the top semicircles)

So, 12+Diameter+12=60

Diameter = 36

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Re: If the 5 semicircles shown above are identical, what is the diameter  [#permalink]

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22 Jun 2020, 11:13
3D+24=2D+60

D = 36

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Re: If the 5 semicircles shown above are identical, what is the diameter  [#permalink]

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22 Jun 2020, 11:56
1
22 + a = a + 12 + b = b + 16 + c = c + 12 + d = d + 22

From first 2 equation, b =10.
Substituting the value of b in equation 3 and 4,
c + 26 = c + 12 + d
d = 14.
So, diameter, d + 22 = 14 + 22 = 36

Re: If the 5 semicircles shown above are identical, what is the diameter   [#permalink] 22 Jun 2020, 11:56