From the given figure, prove that : \[\mathrm{AP}+\mathrm{BQ}+\mathrm{CR}=\mathrm{BP}+\mathrm{CQ...

From the given figure, prove that :
\[\mathrm{AP}+\mathrm{BQ}+\mathrm{CR}=\mathrm{BP}+\mathrm{CQ}+\mathrm{AR} \text {. }\]
Also, show that :
\( \mathrm{AP}+\mathrm{BQ}+\mathrm{CR}=\frac{1}{2} \times \) Perimeter of \( \triangle \mathrm{ABC} \)