# The Perilous Predicament of Gandalf the Grey

**Geometry**Level pending

Saruman has turned bad (when was he never?) and is holding his kidnapped hostage, Gandalf, in Orthanc. Saruman has devised a devious puzzle that Gandalf **must** solve in order to escape safely (that is if Saruman will keep his word). Gandalf knows he can't pull the "eagles-will-save-me" trick again, so to avoid certain death he must solve the puzzle. In the puzzle, Gandalf will be placed in a maze with six smaller congruent circles, such that each circle is tangent to two other circles. All six circles are internally tangent to one giant circle, whose radius is 60 feet. Gandalf's task is to jump from the center of a smaller circle to the center of one of the two tangent circles' center in one stride, and continue this pattern until he has traveled exactly once around the large circle. Without the use of any magical powers, what is the total length of the strides Gandalf must travel to "escape" from Orthanc?