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655-705 (Hard)|   Geometry|      
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Bunuel
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If the 5 semicircles shown above are identical, what is the diameter Mon Jun 22, 2020 2:38 am
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55% (hard)

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63% (02:05) correct 37% (02:25) wrong based on 121 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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If the 5 semicircles shown above are identical, what is the diameter Mon Jun 22, 2020 3:19 am
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Bunuel

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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Answer: Option E

Please check the solution and the Video explanation for step by step solution


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If the 5 semicircles shown above are identical, what is the diameter Mon Jun 22, 2020 3:09 am
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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 Mon Jun 22, 2020 3:33 am
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Bunuel


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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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If the 5 semicircles shown above are identical, what is the diameter Mon Jun 22, 2020 6:06 am
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Bunuel

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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If the 5 semicircles shown above are identical, what is the diameter Mon Jun 22, 2020 11:13 am
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3D+24=2D+60

D = 36

E is the answer.
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If the 5 semicircles shown above are identical, what is the diameter Mon Jun 22, 2020 11:56 am
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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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If the 5 semicircles shown above are identical, what is the diameter Mon Jul 11, 2022 4:51 am
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Using the concept of equating the distance (Which is same)

Let, diameter of identical semicircle be 'd'.

Now, d+12+d+12+d = 22+d+16+d+22 (since the line has same length)

Solving the equation gives d= 36 , Answer E
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If the 5 semicircles shown above are identical, what is the diameter Thu Mar 21, 2024 11:49 am
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