The problem is as follows:
Using the figure from below: Find $PR$. Assume $QS=SR$ and $PQ=24\,cm$ and $TR=8\,cm$.
The alternatives given in my book are as follows:
$\begin{array}{ll} 1.&\textrm{16 cm}\\ 2.&\textrm{32 cm}\\ 3.&\textrm{30 cm}\\ 4.&\textrm{24 cm}\\ 4.&\textrm{18 cm}\\ \end{array}$
This problem has left me confused. I don't know how to use the bisector identities if should they be used here or the triangle congruency. In this particular problem I'm stuck at the very beginning thus I don't know what to do.
Can someone help me here?. As mentioned I think this problem can and should be resolved using triangle congruency but I don't know which of those cases applies in this particular situation. Can someone help me with that?. Please include a drawing in your answer this part is difficult for me and I don't understand. Can you please include a step-by-step solution as I am slow at catching up from reading just lines and maybe this problem requires construction.
