Angle bisector theorem

Here is a result that links angles and proportions: the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.

Theorem — Angle bisector

In a triangle $ABC$, the bisector of the angle $\widehat{C}$ meets the opposite side $AB$ at a point $K$ such that: $\frac{AK}{KB} = \frac{CA}{CB}.$ The bisector divides the opposite side into parts proportional to the adjacent sides.

Links

Topics: Euclidean circle
Concepts: Bisector · Line
Skills: Synthetic geometry