If the angle of intersection at a point where the two circles with radii $5 \mathrm{~cm}$ and $12 \mathrm{~cm}$ intersect is $90^{\circ}$, then the length (in $\mathrm{cm}$ ) of their common chord is :
Correct Option: , 2
According to the diagram,
In $\Delta P C_{1} C_{2}, \tan \alpha=\frac{5}{12} \Rightarrow \sin \alpha=\frac{5}{13}$
In $\triangle P C_{1} M, \sin \alpha=\frac{P M}{12} \Rightarrow \frac{5}{13}=\frac{P M}{12} \Rightarrow P M=\frac{60}{13}$
In $\Delta P C_{1} M, \sin \alpha=\frac{P M}{12} \Rightarrow \frac{5}{13}=\frac{P M}{12} \Rightarrow P M=\frac{60}{13}$
Hence, length of common chord $(P Q)=\frac{120}{13}$
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