Find AX in the diagram. FIGURE

The Angle Bisector Theorem tells us that ACAX=BCBXso AX=AC BXBC=212428=736 474=18.

jmc

geometry intermediate

Problem

Find

A X

in the diagram.

Solution

The Angle Bisector Theorem tells us that

\frac{A C}{A X} = \frac{B C}{B X}

A X = \frac{A C \cdot B X}{B C} = \frac{21 \cdot 24}{28} = \frac{7 \cdot 3 \cdot 6 \cdot 4}{7 \cdot 4} = 18 .

Final answer