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20 Oct 2010, 09:47
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (01:18) correct
38%
(01:16)
wrong
based on 13
sessions
History
Date
Time
Result
Not Attempted Yet
How to solve this problem? Pls help me
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20 Oct 2010, 10:02
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monirjewel
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. \(15\pi\)
B. \(12\pi\)
C. \(10\pi\)
D. \(7\pi\)
E. \(5\pi\)
A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.
So as ABC is inscribed in semicircle then ABC is a right triangle and AC=diameter=hypotenuse. Also note that the length of arc ABC is half of the circumference.
\(AC=\sqrt{AB^2+BC^2}=\sqrt{64+36}=10\) --> \(radius=\frac{diameter}{2}=\frac{AC}{2}=5\) --> \(circumference=2\pi{r}=10\pi\) --> \(arc_{ABC}=\frac{circumference}{2}=5\pi\).
Answer: E.
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Hi there,
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