Problem of the Week 25

There are ten lines in a plane, each intersecting one another.  No three lines pass through the same point.  At how many points do the lines intersect and into how many regions do they separate the plane?


Alternate Problem 25

A line is numbered from 1 to 610 and fourteen different installations are located at 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, and 610.  A central service station will be built on the line with individual pipelines connected to each of the installations.  Between which two installations should the station be located so that the total length of the pipeline is minimized?


Extension Problem 25

The crescent in the figure is formed by two circles.  The center of the larger circle is C.  The width of the crescent from B to D is 9 units.  The distance from E to F is 5 units.  Assume that FC and BC are perpendicular. What are the diameters of the two circles?