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In the figure above, point B lies on line segment AC

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In the figure above, point B lies on line segment AC  [#permalink]

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New post 05 Nov 2014, 08:46
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In the figure below, point B lies on line segment AC. If the two circular arcs are two semicircles whose diameters are AB and BC, what is the total length of the two arcs?

(1) AB=BC

(2) AC=20
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In the figure above, point B lies on line segment AC  [#permalink]

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New post Updated on: 06 Nov 2014, 06:11
Length of one semicircular arc is \(2*\pi*r\)
So the total length of the arc = \(\pi * AB/2 + \pi * BC/2 = \pi * (AB+BC)/2 = \pi * AC/2\)

So statement 2 is sufficient.

Originally posted by kinjiGC on 05 Nov 2014, 08:48.
Last edited by kinjiGC on 06 Nov 2014, 06:11, edited 3 times in total.
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Re: In the figure above, point B lies on line segment AC  [#permalink]

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Re: In the figure above, point B lies on line segment AC  [#permalink]

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New post 06 Nov 2014, 06:08
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Bunuel wrote:
kinjiGC wrote:
Length of one semicircular arc is \(2pir\)
So the total length of the arc = \(2 * pi * AB + 2 * pi * BC = 2 * pi * (AB+BC) = 2 * pi * AC\)

So statement 2 is sufficient.


How to write \(\pi\): mark \pi and press M button to get \(\pi\)



sorry but, AB is diameter so length of semicircle is 0.5*pi * AB rt?
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Re: In the figure above, point B lies on line segment AC  [#permalink]

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New post 06 Nov 2014, 06:10
anupamadw wrote:
Bunuel wrote:
kinjiGC wrote:
Length of one semicircular arc is \(2pir\)
So the total length of the arc = \(2 * pi * AB + 2 * pi * BC = 2 * pi * (AB+BC) = 2 * pi * AC\)

So statement 2 is sufficient.


How to write \(\pi\): mark \pi and press M button to get \(\pi\)



sorry but, AB is diameter so length of semicircle is 0.5*pi * AB rt?


Good catch. Corrected the error.
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Re: In the figure above, point B lies on line segment AC  [#permalink]

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New post 04 Oct 2018, 21:38
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Re: In the figure above, point B lies on line segment AC   [#permalink] 04 Oct 2018, 21:38
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