A circle is inscribed in $△\mathrm{ABC}$ having sides $8 \mathrm{cm}, 10 \mathrm{cm} \mathrm{and} 12 \mathrm{cm}$ as shown in figure. Find $\mathrm{AD}, \mathrm{BE}$ and $\mathrm{CF}$.

In figure, $\mathrm{O}$ is the centre of the circle with radius $5 \mathrm{cm}$. $\mathrm{T}$ is the point such that $\mathrm{OT}=13 \mathrm{cm}$ and $\mathrm{OT}$ intersects the circle at $\mathrm{E}$. If $\mathrm{AB}$ is the tangent to the circle at $\mathrm{E}$ and the length of $\mathrm{AB}$ is $\frac{p}{q} \mathrm{cm}$, then find the value of $\frac{p}{q}$.

An artist has created a triangular stained-glass window and has one strip of small length left before completing the window. She needs to figure out the length of the left out portion based on the lengths of the other sides as shown in the figure. If the length of the remaining one strip is $k \mathrm{cm}$, then find the value of $k$.