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In the figure shown, the triangle is inscribed in the [#permalink]

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25 Jan 2006, 09:29

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E

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71% (01:29) correct
29% (00:30) wrong based on 35 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

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If a triangle is inscribed in a semi-circle, it will always be a right angle triangle with right angle at the corner which touches the arc portion of semi-circle (Like angle ABC here).
_________________

If a triangle is inscribed in a semi-circle, it will always be a right angle triangle with right angle at the corner which touches the arc portion of semi-circle (Like angle ABC here).

Thank you for this. E is the answer.
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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 8-6-10 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: In the figure shown, the triangle is inscribed in the [#permalink]

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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 AB-BC=8-6=2. So, 2<AC<14 Circumference of ABC=2πr/2--->πr If r=highest 7, then length of ABC=7π But it is actually less than 7π. So, E is correct answer. _________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow

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Re: In the figure shown, the triangle is inscribed in the
[#permalink]
17 Nov 2016, 08:18