G9.1 The lengths of the 3 sides of $\triangle L M N$ are 8,15 and 17 respectively.
If the area of $\triangle L M N$ is $A$, find $A$.

G9.2 If $r$ is the length of the radius of the circle inscribed in $\triangle L M N$, find $r$.
$$
8^{2}+15^{2}=64+225=289=17^{2}
$$
$\therefore \triangle L M N$ is a right-angled triangle
$$
A=\frac{8 \times 15}{2}=60
$$

Reference: 1989 HG9
Let $O$ be the centre and the radius of the circle be $r$, which touches the triangle at $C, D$ and $E$.
$O C \perp L M, O D \perp M N, O E \perp L N$ (tangent $\perp$ radius)
$O D M C$ is a rectangle (which consists of 3 right angles)
$$
O C=r=O D \text { (radii) }
$$
$\Rightarrow O C M D$ is a square.
$$
\begin{array}{l}
C M=M D=r \text { (opp. sides, rectangle) } \\
L C=15-r, N D=8-r \\
L E=L C=15-r, N E=N D=8-r \text { (tangent from ext. pt.) } \\
L E+N E=L N \\
\Rightarrow 15-r+8-r=17 \\
\Rightarrow r=3
\end{array}
$$