Hi All,
In this prompt, we are told that a triangle is INSCRIBED in a semi-circle (which means that all 3 points of the triangle are ON the circumference of the half-circle) – and we are given the lengths of the two shorter sides of the triangle (6 and 8). We’re asked for the ARC LENGTH of the semi-circle.
To answer this question, we’ll clearly need the radius of the semi-circle. There is also one specific math rule that we’ll need to know: when a triangle is inscribed in a circle – AND one of the sides is the DIAMETER of the circle – then we have a RIGHT TRIANGLE.
Since triangle ABC is a right triangle and the two ‘legs’ are 6 and 8, we have a 3/4/5 right triangle that has been ‘doubled’ (meaning that the sides are 6, 8 and 10). By extension, the diameter of the semi-circle is 10 and the radius is 5.
Circumference of a Circle is based on the formula:
C = (2)(pi)(Radius)
A semi-circle is half of a circle, so once we have the full circumference, we can divide that by 2 to find the arc length here:
(2)(pi)(5) / 2 = 5pi
Final Answer: E
GMAT Assassins aren’t born, they’re made,
Rich
