Solve the equation $\sqrt {a-\sqrt{a+x}}=x$ in real numbers in terms of the real number $a>1$.

Let $ABC$ be a triangle with $|AB|=|AC|=26$, $|BC|=20$. The altitudes of $\triangle ABC$ from $A$ and $B$ cut the opposite sides at $D$ and $E$, respectively. Calculate the radius of the circle passing through $D$ and tangent to $AC$ at $E$.

$1$ or $-1$ is written in $50$ letters. These letters are put into $50$ envelopes. If you ask, you can learn the product of numbers written into any three letters. At least, how many questions are required to find the product of all of the $50$ numbers?