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In the adjoining figure, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.

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

∴ PR × PS = PQ2 [Tangent secant segments theorem]

∴ 8 × PS = 122 

∴ 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

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