Firstly, OS is the radius of the circumference. So, OS = OR = OT = OP. So:
[tex]OQ=TQ-OT=TQ-OS=50-16=34[/tex]Similarly, we can find RQ by:
[tex]RQ=OQ-OR=OQ-OS=34-16=18[/tex]Because QS is tangent to the circumference, the angle m[tex]\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}[/tex]So, OQ = 34, QS = 30 and RQ = 18.
