Solve the following two equations for $r $ and $x$:

$$

\left(\sqrt{16-x^2}-r\right)^2
+\left(x-2 \sqrt{2}
\sqrt{r}\right)^2=r^2\
\left(x-2 \sqrt{2}
\sqrt{r}\right)-\frac{ x
\left(\sqrt{16-x^2}-r\right
)}{\sqrt{16-x^2}}=0

$$

Question

Solve the following two equations for $r $ and $x$:

$$

\left(\sqrt{16-x^2}-r\right)^2
   +\left(x-2 \sqrt{2}
   \sqrt{r}\right)^2=r^2\
 \left(x-2 \sqrt{2}
   \sqrt{r}\right)-\frac{ x
   \left(\sqrt{16-x^2}-r\right
   )}{\sqrt{16-x^2}}=0

$$

phi · Answer

This is clearly a problem for wolfram.  But if we treat it in the same vein as a crossword or sudoku puzzle, just for the challenge...

anonymous · Answer

@phi I agree that wolfram will give the same answer. Your method is very nice.