If some point is taken outside a circle, and two straight lines radiate from it towards the circle, and (one) of them cuts the circle, and the (other) touches (it), then the (rectangle contained) by the whole (straight line) cutting (the circle), and the (part of it) cut off outside (the circle), between the point and the convex circumference, will be equal to the square on the tangent (line).
Let, from a point $D$ outside a given circle, a tangent $DB$ touching the circle at $D$ be drawn and let a secant go through $D$ and cut this circle at the points $C$ and $A$ such that for the lengths segments the inequality $|\overline{DC}|<|\overline{DA}|$ holds. Then $$|\overline{DC}|\cdot |\overline{DA}|=|\overline{DB}|^2.$$
Proofs: 1