Since $AB$ and $AC$ are the tangents from the same point $A$

$\therefore AB=AC=5cm$

Similarly, $BP=PX$ and $XQ=QC$

Perimeter of

\[\Delta APQ=AP+AQ+PQ\]

\[=AP+AQ+(PX+XQ)\]

\[=(AP+PX)+(AQ+XQ)\]

\[=(AP+BP)+(AQ+QC)\]

.\[=AB+AC=5+5=10cm.\]