iran-konkur 2021 Q155

iran-konkur · Other · konkur-riazi_1400_specialized Circles Circles Tangent to Each Other or to Axes
155. Suppose the length of the radical axis of two circles with radii $1 - 6a$ and $6 - 2a^2$ equals 6 units. If the two circles have exactly one common tangent, what is the average of the possible values of $a$?
  • [(1)] $3$
  • [(2)] $\dfrac{13}{3}$
  • [(3)] $6$
  • [(4)] $7$

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\textbf{155.} Suppose the length of the radical axis of two circles with radii $1 - 6a$ and $6 - 2a^2$ equals 6 units. If the two circles have exactly one common tangent, what is the average of the possible values of $a$?

\begin{itemize}
    \item[(1)] $3$
    \item[(2)] $\dfrac{13}{3}$
    \item[(3)] $6$
    \item[(4)] $7$
\end{itemize}



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