Secant–tangent — tangent² = secant · external segment

Dependencies: AA similarity, Tangent–chord angle = inscribed.

Statement

Let $P$ be a point outside $\odot O$. From $P$ draw a tangent $PT$ (touching at $T$), and a secant meeting the circle at $A$ and $B$ ($A$ closer, $B$ farther). Then

That is, from a point outside the circle, "the square of the tangent length" equals "the product of the two secant segments (external × full)".