Difference between revisions of "1983 AIME Problems/Problem 4"
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Revision as of 22:57, 23 July 2006
Problem
A machine shop cutting tool is in the shape of a notched circle, as shown. The radius of the circle is 50 cm, the length of is 6 cm, and that of is 2 cm. The angle is a right angle. Find the square of the distance (in centimeters) from to the center of the circle. [img]http://www.artofproblemsolving.com/Forum/album_pic.php?pic_id=790&sid=cfd5dae222dd7b8944719b56de7b8bf7[/img] Template:Img
Solution
Because we are given a right angle, we look for ways to apply the Pythagorean Theorem. Extend a perpendicular from to and label it . Additionally, extend a perpendicular from to the line , and label it . Let and . We're trying to find .
Applying the Pythagorean Theorem, , and .
Thus, , and . We solve this system to get and , resulting in an answer of .