G7.1 In the figure, $Q R, R P, P Q$ are 3 arcs, centres at $A, B, C$ respectively, touching one another at $R, P, Q$. If $A R=r, R B=6$, $Q C=4, \angle A=90^{\circ}$, find $r$.
$\begin{array}{l}A Q=r, C P=4, B P=6 \\ A B=r+6, A C=r+4, B C=4+6=10 \\ A B^{2}+A C^{2}=B C^{2} \\ \Rightarrow(r+6)^{2}+(r+4)^{2}=10^{2} \\ 2 r^{2}+20 r-48=0 \\ r^{2}+10 r-24=0 \\ (r-2)(r+12)=0 \\ r=2\end{array}$