Question

61 pointFind the value of r. Qis the point of tangency.Q 4 S2r=type your answer...

Answer 1

Step 1

State Pythagoras theorem

`\text{Hypothenuse}^2=adjacent^2+opposite^2`

Hypothenuse = r+2 = radius + 2

adjacent = r = radius

opposite = 4 = QS

Step 2

Substitute and find the value of r

`\begin{gathered} (r+2)^2=r^2+4^2 \\ (r+2)(r+2)=r^2+16 \end{gathered}`
`\begin{gathered} r^2+2r+2r+4=r^2\text{ + 16} \\ r^2+4r+4=r^2+16 \end{gathered}`
`\begin{gathered} r^2-r^2\text{ + 4r = 16-4} \\ 4r\text{ = 12} \\ r\text{ = }(12)/(4) \\ r=\text{ 3} \end{gathered}`

Hence r = 3