In $\Delta ABC$,$\overline{AM}$ and $\overline{CN}$ are altitudes. If $AB = 12$,$BC = 15$ and $AM = 9.6$,then $CN = \ldots$

In $\Delta PQR$,$\angle Q$ is a right angle. If $PQ = 8$ and $QR = 15$,then the radius of a circle touching all the three sides of $\Delta PQR$ is $\ldots \ldots.$

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 10$,$BC = 16$ and $AD = \sqrt{58}$,find $AC$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $AM - CM = 10$ and $AB^{2} - BC^{2} = 260$,find $AC$.

In $\Delta PQR$,$\overline{PM}$ is a median. If $PQ^{2} + PR^{2} = 148$ and $PM = 7$,find $QR$.

In $\Delta ABC$,$m \angle B = 90^\circ$. If $AC - AB = 27$ and $AC - BC = 6$,find the perimeter of $\Delta ABC$.