# How do I find the modulus of a sum of vectors which is part of a triangle embedded in a quarter a circle?

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#### Chemist116

The problem is as follows:

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?.

Math Team