Question

bd is an angle bisector of ∠abc. find cd.
a
9x + 3
b
d
c
6x + 21
cd = ?

Explanation:

Step1: Apply Angle Bisector Theorem

$\frac{AD}{CD} = \frac{AB}{BC}$
Since $BD$ bisects $\angle ABC$ and is perpendicular to both $AB$ and $BC$, $AB=BC$, so $AD=CD$.

Step2: Set up equation

$9x + 3 = 6x + 21$

Step3: Solve for x

$9x - 6x = 21 - 3$
$3x = 18$
$x = 6$

Step4: Calculate CD

$CD = 6x + 21 = 6(6) + 21 = 36 + 21 = 45$

Answer:

45