In the figure above, the points A and C are diametrically opposite on

Two ways.

First, the way I would do it on the test. It takes 20 seconds and I am positive I won't make a silly mistake.
LOOK at the drawing. Is the distance walking around the edge of the lake less than, the same as, or greater than the distance walking on the bridges? It's greater. How much greater? I don't know, but not much; certainly less than twice as much. Now look at the answer choices.
A. 3/4 ... Nope.
B. 2.8/pi ... Nope.
C. 4.2/4 ... Keep it.
D. 6/3 ... Nope.
E. 3 ... Nope.
Answer choice C.

Second, the way that many people on here seem to like better and give more kudos ...even though is both slower AND comes with a higher risk of making a silly mistake
Make OC = 1. The circumference is 2pi. Walking around the edge of the lake is pi.
ABC is a 45-45-90 with a hypotenuse of 2. The legs are each \(\sqrt{2}\).
The ratio is therefore \(\frac{pi}{2\sqrt{2}} = \frac{pi\sqrt{2}}{4}\).
Answer choice C.


ThatDudeKnowsBallparking