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# If the diameter of the circle is 36, what is the length of arc ABC?

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If the diameter of the circle is 36, what is the length of arc ABC? [#permalink]
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Bunuel wrote:

If the diameter of the circle is 36, what is the length of arc ABC?

(A) $$8$$

(B) $$8\pi$$

(C) $$28\pi$$

(D) $$32\pi$$

(E) $$56\pi$$

Attachment:
The attachment Capture.JPG is no longer available

Diameter = 36
i.e. radius = 36/2 = 18

Refer to Property attached in Image 1 which says that angle at the circumference is Half of the angle at the centre drawn by the same arc

Refer to image 2, If angle at circumference = 40 then angle at centre = 2*40 = 80º

Now, Length of Minor Arc AC $$= (Angle at centre/360)*2πr = (80º/360º)*2*π*18 = 8π$$

Total Circumference $$= 36π$$

i.e. Major Arc ABC$$= 36π-8π = 28π$$

Attachments

File comment: Angle at centre will be 2*40 = 80

2.jpeg [ 5.71 KiB | Viewed 13861 times ]

File comment: www.GMATinsight.com

1.jpg [ 12.36 KiB | Viewed 13841 times ]

Originally posted by GMATinsight on 20 Sep 2018, 04:16.
Last edited by GMATinsight on 18 Oct 2018, 04:22, edited 1 time in total.
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Re: If the diameter of the circle is 36, what is the length of arc ABC? [#permalink]
Bunuel Hi Bunuel, how do we know for sure which Arc is the question asking to calculate? I was confused between minor and major arc, because saying arc ABC it can refer to both in my opinion. THank you
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Re: If the diameter of the circle is 36, what is the length of arc ABC? [#permalink]
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VodkaHelps wrote:
Bunuel Hi Bunuel, how do we know for sure which Arc is the question asking to calculate? I was confused between minor and major arc, because saying arc ABC it can refer to both in my opinion. THank you

Length fo Arc ABC can be understood in only one way like it has been interpreted here.

Always identify the arc by reading the points in that particular order.

Arc AC could have caused two interpretations which you intend to bring here but when we say are ABC then it's only the major arc that is being referred.

I hope this helps!!!
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Re: If the diameter of the circle is 36, what is the length of arc ABC? [#permalink]
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Bunuel wrote:

If the diameter of the circle is 36, what is the length of arc ABC?

(A) $$8$$

(B) $$8\pi$$

(C) $$28\pi$$

(D) $$32\pi$$

(E) $$56\pi$$

Solution:

We see that the circumference of the circle is C = 2πr = 2π(18) = 36π. Since angle ABC is an inscribed angle of minor arc AC, arc AC is twice the measure of angle ABC, or 80 degrees. Thus, major arc ABC is 360 - 80 = 280 degrees, and we can create the equation where x is the length of arc ABC:

280/360 = x/36π

28/36 = x/36π

36x = 28 * 36π

x = 28π

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Re: If the diameter of the circle is 36, what is the length of arc ABC? [#permalink]
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Re: If the diameter of the circle is 36, what is the length of arc ABC? [#permalink]
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