OE


The two perimeters share the line BC, therefore, you can recast this question:

A. The combined length of two radii (AB and AC)

B. The length of arc BDC

The easiest thing to do in this situation is use numbers. Assume the radius of the circle is 2. If the radius is 2, then you can rewrite Quantity A is 4

Now you need to figure out the length of arc BDC if the radius is 2. You can set up a proportion, because the ratio of central angle to 360° will be the same as the ratio of the arc length to the circumference:

120/360=1/3

Circumference is \(2 \pi r\)

\(C=2 \pi (2) = 4 \pi\)


Arc length is 1/3 so it is \(\frac{4 \pi}{3}\)

So B >A