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

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

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New post 22 Jun 2020, 02:38
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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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New post 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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New post 22 Jun 2020, 03:19
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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



Answer: Option E

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

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New post 22 Jun 2020, 03:33
1
Bunuel wrote:
Image

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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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New post 22 Jun 2020, 06:06
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Bunuel wrote:
Image
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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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

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

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

D = 36

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

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New post 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

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

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

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