1962 AHSME Problems/Problem 25
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Problem
Given square with side
feet. A circle is drawn through vertices
and
and tangent to side
. The radius of the circle, in feet, is:
Solution
Let be the center of the circle and
be the point of tangency of the circle and
and let
be the point of intersection of lines
and
Because of the symmetry,
feet. Let the length of
be
. The length of
is
. By Pythagorean Theorem,
. Because
,
, and
are radii of the same circle,
. So,
. Squaring both sides, we obtain
. Subtracting
from both sides and adding
, our equation becomes
, so our answer is
.