In $\Delta PQR, m \angle Q = 90^{\circ}$. If $PR = 17$ and $PQ = 8$,then $QR = \ldots$

In $\Delta PQR$,$m\angle Q = 90^{\circ}$,$PR = a^{2} + b^{2}$ and $QR = a^{2} - b^{2}$. Then,$PQ = \ldots$ $(a, b \in R^{+}; a > b)$

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QD}$ is an altitude. If $PD = 9RD$,prove that $PQ = 3QR$.

In quadrilateral $ABCD$,a line through $A$ intersects $BD$ at $L$,$CD$ at $M$,and the extension of $BC$ at $N$. Prove that $\frac{LD^2}{LB^2} = \frac{LM}{LN}$.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = x$,$MB = x-2$,$AN = x+2$ and $NC = x-1$,find the value of $x$.

In the given figure,if $PQRS$ is a parallelogram and $AB \parallel PS$,then prove that $OC \parallel SR$.