Difference between revisions of "1983 AIME Problems/Problem 4"
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Revision as of 23:57, 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]
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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
.