G1.1 If the area of a given sector $s=4 \mathrm{~cm}^{2}$, the radius of this sector $r=2 \mathrm{~cm}$ and the arc length of this sector $A=p \mathrm{~cm}$, find the value of $p$.

G1.2 Given that $\frac{a}{2 b+c}=\frac{b}{2 c+a}=\frac{c}{2 a+b}$ and $a+b+c \neq 0$. If $q=\frac{2 b+c}{a}$, find the value of $q$.
G1.3 Let $A B C$ be a right-angled triangle, $C D$ is the altitude on $A B, A C=3$, $D B=\frac{5}{2}, A D=r$, find the value of $r$.

G1.4 If $x^{3}+p x^{2}+q x+17 \equiv(x+2)^{3}+a$, find the value of $a$.
By the formula $A=\frac{1}{2} r s$, where $A$ is the sector area, $r$ is the radius and $s$ is the arc length
$$
\begin{aligned}
4 & =\frac{1}{2}(2) p \\
p & =4
\end{aligned}
$$

Let $\frac{a}{2 b+c}=\frac{b}{2 c+a}=\frac{c}{2 a+b}=k$
$a=(2 b+c) k ; b=(2 c+a) k ; c=(2 a+b) k$
$a+b+c=(2 b+c+2 c+a+2 a+b) k$
$a+b+c=(3 a+3 b+3 c) k \Rightarrow k=\frac{1}{3}$
$q=\frac{2 b+c}{a}=\frac{1}{k}=3$
$A D=A C \cos A=\frac{3 A C}{A B}=\frac{9}{\frac{5}{2}+A D}$
$\frac{5}{2} A D+A D^{2}=9$
$$
\begin{array}{l}
2 A D^{2}+5 A D-18=0 \\
(2 A D+9)(A D-2)=0 \\
A D=r=2
\end{array}
$$

Compare the constant term: $17=8+a$
$$
a=9
$$