Tangent Segment Length to Circle

Consider a circle with radius $r$. A point $P$ is located outside the circle such that the distance from the center of the circle, $O$, to the point $P$ is $d$, where $d > r$. A tangent line is drawn from point $P$ to the circle, touching the circle at point $T$. Let the distance from point $P$ to the point of tangency $T$ be denoted as $PT$.

Using the properties of circles and right triangles, determine the relationship between the quantities described:

Quantity A: The length of the line segment $PT$.

Quantity B: The difference between the distance $d$ and the radius $r$, expressed as $d - r$.

Use the formula for the tangent from a point to a circle, which states that $PT = ext{sqr}(d^2 - r^2)$.