Problem: Equilateral triangle (See figure) with side of length inches is placed inside square with side of length inches so that is on side . The triangle is rotated clockwise about , then , and so on along the sides of the square until returns to its original position. The length of the path in inches traversed by vertex is equal to
Answer Choices:
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Solution:
The point returus to its original position after moves. In of these moves, the rotation is about vertex with no path traversed by . In the other moves, are about a mid-point of a side of the gquare with the radius to sweeping through or radians, and are about a corner of the square with the radius to sweeping through or radians. The total angle swept through by the radius to is radians. Hence the length of the path traversed by is inches. The general solution is: