take a look at the Angle Bisector Theorem
AX/BX = CA/CB
Find AX in the diagram if CX bisects angle ACB.
And then there's a diagram below with triangle ABC, where X is on line C, BC=45, AC=21, and BX=30.
2 answers
This is really just about the base toes of a triangle, namely triangle ABC. This is the complete solution for this particular problem:
The Angle Bisector Theorem tells us that \[\frac{AC}{AX}=\frac{BC}{BX}\]so \[AX=\frac{AC\cdot BX}{BC}=\frac{21\cdot30}{45}=\boxed{14}.\]
The Angle Bisector Theorem tells us that \[\frac{AC}{AX}=\frac{BC}{BX}\]so \[AX=\frac{AC\cdot BX}{BC}=\frac{21\cdot30}{45}=\boxed{14}.\]