Carcass wrote:
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
B. 6π
C. 7π
D. 8π
E. 10 π
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 =
10Circumference of COMPLETE circle = (DIAMETER)(π)
So, circumference of SEMIcircle = (DIAMETER)(π)/2
= (
10)(π)/2
= 5π
= A
Cheers,
Brent