Two young men in tuxedos are walking down the street at about 10 pm. One is carrying a round goldfish bowl filled with water. There is a goldfish, named Gertrude, in the bowl. As they pass a round pool in the park, the goldfish gets overexcited and jumps out of the bowl into the pool, right at the edge. She starts swimming due north. She hits a wall after she has swum exactly 30 feet. She heads east, and, after going 40 feet, she hits a wall again. Once she regains consciousness after the second collision, she calculates the diameter of the pool (Gertrude is a clever goldfish).
What is the diameter of the pool? And what is up with those two guys in tuxes?
Solution
Gertrude has swum the sides of an inscribed angle, and since it’s a right angle, her starting and ending points (A and C, see the figure) are the endpoints of a diameter of the pond. AC = 50 feet.
(The first two sentences of this problem describe a scene I actually saw. I regret that I didn't ask them what they were up to. The part about Gertrude is made up.)
