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

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25 Jan 2006, 10:29

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69% (01:32) correct
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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).
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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).

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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