Question 3
A right triangle with hypotenuse $a$ stands on its shorter side $c=1$. We rotate it sequentially three times as it is shown below. The diagram labels $a>b>c$.
If $TS$ is a common tangent of the three arcs, find $a$.
Answer format: enter an exact expression; sqrt(n) denotes a square root.
If $TS$ is a common tangent of the three arcs, find $a$.
Answer format: enter an exact expression; sqrt(n) denotes a square root.