Question

I need haelp on this question

Answer 1

Firstly, OS is the radius of the circumference. So, OS = OR = OT = OP. So:

`OQ=TQ-OT=TQ-OS=50-16=34`

Similarly, we can find RQ by:

`RQ=OQ-OR=OQ-OS=34-16=18`

Because QS is tangent to the circumference, the angle m
`\begin{gathered} OQ^2=OS^2+QS^2 \\ 34^2=16^2+QS^2 \\ QS^2=34^2-16^2=1156-256=900 \\ QS=\sqrt[]{900}=30 \end{gathered}`So, OQ = 34, QS = 30 and RQ = 18.