Solution
Step 1
State Pythagoras theorem
[tex]\text{Hypothenuse}^2=adjacent^2+opposite^2[/tex]
Hypothenuse = r+2 = radius + 2
adjacent = r = radius
opposite = 4 = QS
Step 2
Substitute and find the value of r
[tex]\begin{gathered} (r+2)^2=r^2+4^2 \\ (r+2)(r+2)=r^2+16 \end{gathered}[/tex][tex]\begin{gathered} r^2+2r+2r+4=r^2\text{ + 16} \\ r^2+4r+4=r^2+16 \end{gathered}[/tex][tex]\begin{gathered} r^2-r^2\text{ + 4r = 16-4} \\ 4r\text{ = 12} \\ r\text{ = }\frac{12}{4} \\ r=\text{ 3} \end{gathered}[/tex]
Hence r = 3
