Problem: In this figure the radius of the circle is equal to the altitude of the equilateral triangle . The circle is made to roll along the side , remaining tangent to it at a variable point and intersecting sides and in variable points and , respectively.
Let be the number of degrees in arc . Then , for all permissible positions of the circle:
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Answer Choices:
A. varies from 30 to 90
B. varies from 30 to 60
C. varies from 60 to 90
D. remains constant at 30
E. remains constant at 60
Solution:
Consider position is measured by : so that . In any other position, such as II, is still measured by . Since remains unchanged at , remains unchanged at .
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