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06 Mar 2016, 17:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
77% (01:10) correct
23%
(01:24)
wrong
based on 188
sessions
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Attachment:
Triangle ABC.jpg [ 4.01 KiB | Viewed 11987 times ]
A. 5π(pi)
B. 6π(pi)
C. 7π(pi)
D. 8π(pi)
E. 10 π(pi)
* A solution will be posted in two days.
Updated on: 30 Apr 2018, 10:04
Originally posted by BrentGMATPrepNow on 07 Mar 2016, 12:24.
Last edited by BrentGMATPrepNow on 30 Apr 2018, 10:04, edited 1 time in total.
Last edited by BrentGMATPrepNow on 30 Apr 2018, 10:04, edited 1 time in total.
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MathRevolution
Attachment:
Triangle ABC.jpg
If the triangle ABC is inscribed in semi-circle BAC as above figure and BC is a diameter, the length of AB is 6 and the length of AC is 8, what is the length of arc BAC?A. 5π(pi)
B. 6π(pi)
C. 7π(pi)
D. 8π(pi)
E. 10 π(pi)
Since BC is the diameter of the semi-circle, we know that ∠BAC is 90º
In other words, we can conclude that BAC is a RIGHT TRIANGLE and side BC is the HYPOTENUSE.
This means we can apply the Pythagorean Theorem to get: 6² + 8² = (side BC)²
Simplify: 36 + 64 = (side BC)²
Simplify: 100 = (side BC)²
So, side BC = 10
In other words, the DIAMETER = 10
Circumference of COMPLETE circle = (DIAMETER)(π)
So, circumference of SEMIcircle = (DIAMETER)(π)/2
= (10)(π)/2
= 5π
= A
Cheers,
Brent
General Discussion
07 Mar 2016, 05:40
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BC is the diameter. Triangle ABC is right angled at A. If AB = 6 and AC = 8 then BC = 10
Radius = 10/2 = 5.
Length of arc BAC = Circumference/2 = pi * r = 5 * pi
Answer: A
Radius = 10/2 = 5.
Length of arc BAC = Circumference/2 = pi * r = 5 * pi
Answer: A
