Difference between revisions of "1972 AHSME Problems/Problem 23"
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Problem 23
The radius of the smallest circle containing the symmetric figure composed of the 3 unit squares shown above is
//draw((0,0)--(0,1)--(2,1)--(2,0)--cycle^^(.5,1)--(.5,2)--(1.5,2)--(1.5,1)--cycle^^(1,2)--(1,0)--cycle^^(.5,2)--(1,13/16)--);
Solution 1
Draw lines from points and
to the center of the circle
. As shown from the diagram,
is the radius of the circumscribed circle. Set
to
, so as
is
,
is
. Then,
and
are both right, so an equation can be formed with the Pythagorean Theorem. The radii (hypotenuses) are equal, so the following equation can be made and solved:\
is solved, so plugging it in to the original formula yields:
~airbus-a321