i. Ray PQ is a tangent to the circle at point Q and seg PS is the secant. [Given]

∴ PR × PS = PQ^{2} [Tangent secant segments theorem]

∴ 8 × PS = 12^{2}

∴ 8 × PS = 144

∴ PS = 144/8

∴ PS = 18 units

ii. Now, PS = PR + RS [P – R – S]

∴ 18 = 8 + RS

∴ RS = 18 – 8

∴ RS = 10 units