Secant-tangent theorem

The secant tangent theorem (also tendon tangent set called ) is a theorem of Euclidean geometry. He describes what relationship tracks are formed by a tangent, a secant and the associated circuit (see drawing).

Given a circle, let k be a secant and a tangent t g, which intersect at a point S outside the circle. If we denote the intersection points of the circle k with g as the point of contact of the tangent respectively, and as such the following applies:

This statement can also be formulated as a ratio equation:

The secant tangent theorem can be - like the tendons and set the Sekantensatz - prove using similar triangles.