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jmc

geometry intermediate

Problem

A greeting card is 6 inches wide and 8 inches tall. Point A is 3 inches from the fold, as shown. As the card is opened to an angle of 45 degrees, through how many more inches than point A does point B travel? Express your answer as a common fraction in terms of .
problem
Solution
Point A is traveling along the circumference of a circle with a diameter of 6 inches. This circumference is inches. Point B is traveling along the circumference of a circle with a diameter of 12 inches. This circumference is inches. Both points travel 45 degrees, which is of the circles' circumferences. The difference is then .
Final answer
\frac{3}{4}\pi\text{ inches}