In the figure from below, calculate the modulus of $\vec{x}+\vec{y}$. $P$ is tangential point. Show the answer in terms of $R$.

The alternatives are as follows:

$\begin{array}{ll}

1.&1R\\

2.&0.41R\\

3.&0.59R\\

4.&1.41R\\

5.&2.12R\\

\end{array}$

The only thing which I was able to spot here was to establish that

$x=\frac{(R+a)\sqrt{2}}{2}+a$

$y=\frac{(R+a)\sqrt{2}}{2}+a$

But this doesn't seem very convincing to me. How exactly can I use the vector decomposition in this set of vectors?. Does it exist a way to solve this graphically without requiring algebra?. Can somebody help me here?.