# CAT 2013 | Question: 17

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In a triangle $\text{PQR, PQ} = 12$ cm and $\text{PR} = 9$ cm and $\angle \text{Q} +\angle \text{R}=120^{\circ}$. If the angle bisector of $\angle \text{P}$ meets $\text{QR}$ at $\text{M}$, find the length of $\text{PM}$

1. $\dfrac{28\sqrt5}{9}$ cm
2. $\dfrac{42\sqrt5}{11}$ cm
3. $\dfrac{36\sqrt3}{7}$ cm
4. $4\sqrt3$

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