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The figure above represents a bicycle path. If the semicircular portio

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The figure above represents a bicycle path. If the semicircular portio  [#permalink]

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New post 14 Nov 2017, 23:47
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A
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C
D
E

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  35% (medium)

Question Stats:

67% (01:43) correct 33% (01:36) wrong based on 32 sessions

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The figure above represents a bicycle path. If the semicircular portion ABC is 100π meters long and portion CD is 100 meters long, how many meters long is portion AD?

(A) 150
(B) 200
(C) 50π
(D) 100√2
(E) 100√3


Attachment:
2017-11-15_1036_002.png
2017-11-15_1036_002.png [ 11.37 KiB | Viewed 575 times ]

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Re: The figure above represents a bicycle path. If the semicircular portio  [#permalink]

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New post 15 Nov 2017, 01:17
P*d/2=100*P
d=200=AC
Using Pythagorean equation:
AD^2=200^2-100^2=(200-100)*(200+100)=100*300=30000
AD=3^1/2*10*10=100*3^1/2
Answer E.
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Re: The figure above represents a bicycle path. If the semicircular portio  [#permalink]

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New post 15 Nov 2017, 09:41
Bunuel wrote:
Image
The figure above represents a bicycle path. If the semicircular portion ABC is 100π meters long and portion CD is 100 meters long, how many meters long is portion AD?

(A) 150
(B) 200
(C) 50π
(D) 100√2
(E) 100√3


Attachment:
2017-11-15_1036_002.png


circumference of semicircle = pi(r) = 100 (pi)
r = 100 meters
given CD = 100 and diameter AC subtends an angle of 90 degree. This means D lie on the circle.
using PGT, AD = 100√3
---E---
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Re: The figure above represents a bicycle path. If the semicircular portio  [#permalink]

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New post 15 Nov 2017, 10:53
Bunuel wrote:
Image
The figure above represents a bicycle path. If the semicircular portion ABC is 100π meters long and portion CD is 100 meters long, how many meters long is portion AD?

(A) 150
(B) 200
(C) 50π
(D) 100√2
(E) 100√3


Attachment:
The attachment 2017-11-15_1036_002.png is no longer available

Attachment:
2017-11-15_1036_002.png
2017-11-15_1036_002.png [ 11.37 KiB | Viewed 350 times ]

\(πr = 100π\)

So, \(r = 100\)

Or, \(AC = 200\)

In Δ ADC

\(AC^2 = AD^2 + CD^2\)

\(200^2 = AD^2 + 100^2\)

Or, \(AD^2 = 200^2 - 100^2\)

Or, \(AD = \sqrt{300*100}\)

Or, \(AD = 100\sqrt{3}\) answer will be (E)
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Re: The figure above represents a bicycle path. If the semicircular portio &nbs [#permalink] 15 Nov 2017, 10:53
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