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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Jun 2017
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Lima, Peru
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?.
 

romsek

Math Team
Sep 2015
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Please don't ask questions twice.
 

greg1313

Forum Staff
Oct 2008
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Duplicate. Thread closed. See here for further discussion.
 
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