The fifth Problem Of the Week has now been posted at the big website. I've also posted an “official” solution to Problem Four. POTW will be taking two weeks off after this one, so you will have to make this last. (Spring break is almost upon us, which seems incredible considering how cold it is outside.)
In other news, I see that Jerry Coyne is spotlighting the videos of British comedian Philomena Cunk, such as this one about evolution:
Great stuff! It reminded me of this old Bob and Ray routine about the Komodo dragon:
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Philomena, not Philomina, and her *actual* name is Diane Morgan. I'm not sure about Philomena, but Cunk is certainly not a real surname, one of the other people on the show was Barry Shitpeas.
Thanks for pointing out the typo, which I have corrected. I'm aware that Philomena Cunk is not her real name, but it is the name she performs under in these videos, so it seemed appropriate to use it.
Her one on Philosophy is brilliant.
Only 1,815 views. Now we know what's wrong with the world!
Still a pretty easy one. Let C be the center of the larger circle. Then angle ABC is a right angle since a tangent of a circle is perpendicular to the radius. By the Pythagorean theorem then, AC^2 = AB^2 + BC^2. BC is the radius of the larger circle, which is 3, and AB is given as 5. Thus, AC^2 = 9+25=34. AC = sqrt(34). AC is the sum of the two radii, so the radius of the smaller circle must then be sqrt(34)-3.
Sean's answer is right, but I wanted to point out that the "SAT/GRE" approach I talked about in one of the previous POTW threads would throw you off here because you'd want to find ways to make a 3-4-5 right triangle out of the information given, and then founder on trying to connect it to the larger circle somehow. You could waste 30 seconds or so looking for the easy answer in a problem where direct analysis clearly goes faster.
#5: Yep using 3 and 5 introduces something of a psychological trick to it. Also, the fact that envisioning the right triangle in the picture puts it "upside down," i.e., the hypotenuse is on the bottom, not on the left (or right).
Still, these sorts of perceptial problems is kind of what math is for, right? To be able to correct for intuitional mistakes.