Find AX in the diagram if CX bisects ACB. FIGURE

The Angle Bisector Theorem tells us that ACAX=BCBXso AX=AC BXBC=212830=7^23430=7^225=985.

jmc

geometry intermediate

Problem

Find

A X

in the diagram if

C X

bisects

∠ A C B

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 28}{30} = \frac{7 ^{2} \cdot 3 \cdot 4}{30} = \frac{7 ^{2} \cdot 2}{5} = \frac{98}{5} .

Final answer

\frac{98}5