In Figure $\displaystyle 1$, a right triangle ABC in which $\displaystyle \angle \mathrm{B}=90^{\circ}, \mathrm{AB}=12 \mathrm{~cm}$ and $\displaystyle \mathrm{BC}=5 \mathrm{~cm}$ is shown. Find the radius of the circle inscribed in the triangle ABC. Figure $\displaystyle 1$

\(\displaystyle O P B Q\) is a square of side \(\displaystyle r\) \[\text { Also } \quad \begin{aligned} A C= & \sqrt{5^{2}+12^{2}}=13 \\ & \Rightarrow 17-2 r=13 \\ & \Rightarrow r=2 \end{aligned} \] ∴ Radius of circle is $\displaystyle 2$ cm 12. a. Sol. \[\begin{aligned} \text { TSA } & =2 \pi r h+\pi r^{2}+\pi r l \\ & =\frac{22}{7} \times 7[60+7+25] \\ & =2024 \mathrm{~cm}^{2} \end{aligned} \]