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\noindent {\bf Problem statement} The square to the
right is bounded by the lines $x = 1$, $y = 1$, $x = -1$, $y = -1$.
The circle inscribed in the square is the unit circle $x^2 + y^2 = 1$.
Let $C$ be the circle in the upper right hand corner, inscribed in the
region bounded by the lines $x = 1$, $y = 1$, and the unit circle.

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\noindent a)~If $r$ is the radius of $C$, find the center of $C$ in
terms of $r$. ({\it Suggestion:}\/ $C$ is tangent to the lines $x = 1$
and $y = 1$.)

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\noindent b)~Find the distance of the center of $C$ to $(0,0)$ in
terms of $r$. ({\it Suggestion:}\/ $C$ is tangent to the unit circle.)

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\noindent c)~Find $r$ using a) and b), or with some other method.

}

%contributed by Michael O'Nan







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