BREAKING NEWS

## Summary

The intersecting secant theorem or just secant theorem describes the relation of line segments created by two intersecting secants and the associated circle. $\triangle PAC\sim \triangle PBD$ yields
$|PA|\cdot |PD|=|PB|\cdot |PC|$ For two lines AD and BC that intersect each other in P and some circle in A and D respective B and C the following equation holds:

$|PA|\cdot |PD|=|PB|\cdot |PC|$ The theorem follows directly from the fact, that the triangles PAC and PBD are similar. They share $\angle DPC$ and $\angle ADB=\angle ACB$ as they are inscribed angles over AB. The similarity yields an equation for ratios which is equivalent to the equation of the theorem given above:

${\frac {PA}{PC}}={\frac {PB}{PD}}\Leftrightarrow |PA|\cdot |PD|=|PB|\cdot |PC|$ Next to the intersecting chords theorem and the tangent-secant theorem the intersecting secants theorem represents one of the three basic cases of a more general theorem about two intersecting lines and a circle - the power of point theorem.