In the following figure, $PAB$ is a secant and $PT$ is a tangent to the circle. If $PT=5\text{ cm}$ and $PA=3\text{ cm}$, then find the measurement of $AB$.

1. According to the Tangent-Secant Theorem for a circle, the square of the tangent segment equals the product of the external secant segment and the entire secant segment:
$$P{T}^2=PA\times PB$$
Substitute the given values $PT=5\text{ cm}$ and $PA=3\text{ cm}$ into the equation:
$$5^2=3\times PB$$
$$25=3\times PB⟹PB=\frac{25}{3}\text{ cm}$$
The total secant length $PB$ is the sum of its segments: $PB=PA+AB$. Solve for $AB$:
$$AB=PB-PA=\frac{25}{3}-3=\frac{25-9}{3}=\frac{16}{3}\text{ cm}$$