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Director
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In the figure shown, the triangle is inscribed in the
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25 Jan 2006, 09:29
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80% (00:35) correct 20% (00:53) wrong based on 142 sessions
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In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC?
A. 15 TT
B. 12 TT
C. 10 TT
D. 7 TT
E. 5 TT == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Director
Joined: 01 Feb 2003
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Location: Hyderabad

as the sides of the triangle are 8 & 6, it is a right angled triangle. Therefore, the diameter of the semi circle(also the third side) is 10.
Answer would be (pie)*R (as it is a semicircle, half the perimeter will be the length of the semicircle) = 5*pie (E)
Regards
Vithal



Director
Joined: 20 Sep 2005
Posts: 998

E.
Another approach:
The third side ( diameter ) should be between (86) and (8+6).
Thus 2 < d < 14.
From the answer choices, 2TTr/2 ( half of the cirumference of circle ) gives
r = 15,12,10,7 and 5 and the corresponding diameter as 30,24,20,14,10.
Only d = 10, satisfies , 2 < d < 14. Thus, the answer is E.



Director
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oa is 5TT
thanks guys, i made a silly error



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cj,
there is a rule:
If a triangle is inscribed in a semicircle, it will always be a right angle triangle with right angle at the corner which touches the arc portion of semicircle (Like angle ABC here).
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GMAT Club Legend
Joined: 07 Jul 2004
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The angle ABC is a right angle (triangle inscribed in semicircle). So lenght of AC = sqrt(64+36) = 10.
Length of the arc ABC = (2* pi * r)/2 = 5pi



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Re: triangle
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11 Sep 2011, 02:48
Quote: cj,
there is a rule:
If a triangle is inscribed in a semicircle, it will always be a right angle triangle with right angle at the corner which touches the arc portion of semicircle (Like angle ABC here). Thank you for this. E is the answer.
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Re: triangle
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11 Sep 2011, 03:48
Its E i.e 5*pi Solution Angle in a semi circle is a right angle and ABC forms a right angle triangle with right angled at B. so AB=8 AND BC=6 so AC=10 as 8610 forms a right angled triangle with Hypotenuse AC so Now we got the diameter =10 and radius =5 Now length of the Segment ABC=circumference/2 i.e 2*pi*r/2 as it is a semicircle so Now length of ABC=Pi*r and from above we know radius=5 so Lenght of segment ABC= 5*pi
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Re: triangle
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11 Sep 2011, 08:36
In a circle, whenever one of the sides of the triangle is diameter, that forms the hypotenuse of the triangle.
AB = 8, BC=6 => AC = 10
Length of arc ABC = (central angle/360)*(2*pi*r)
= (180/360)*(2*pi*r)
= pi*r
AC = 2r = 10 => r = 5
=> Length of arc ABC = 5pi
Answer is E.



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Re: triangle
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12 Sep 2011, 04:07
5*pi is the answer..
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Re: In the figure shown, the triangle is inscribed in the
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17 Nov 2016, 08:18
joemama142000 wrote: In the figure shown, the triangle is inscribed in the semicircle. If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC? A. 15 TT B. 12 TT C. 10 TT D. 7 TT E. 5 TT AC must be between 2 and 14. Because, AB+BC=8+6=14, and ABBC=86=2. So, 2πr If r=highest 7, then length of ABC=7π But it is actually less than 7π. So, E is correct answer.== Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Re: In the figure shown, the triangle is inscribed in the
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18 Jul 2018, 01:59
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Re: In the figure shown, the triangle is inscribed in the &nbs
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