Answer:
C. 6
Explanation:
ΔADC and ΔACB are similar because two of their angles are congruent (∠ACD and ∠ABC, and ∠DAC and ∠CAB)
Because the sides are similar, you can create a proportion
![(AC)/(AD)=(AB)/(AC)](https://img.qammunity.org/2022/formulas/mathematics/college/bju5vu8f1obpc0x92pvgeoc8r0400su1br.png)
substitute the given values for the sides. AD=4 and AB=4+5=9
![(AC)/(4)=(9)/(AC)](https://img.qammunity.org/2022/formulas/mathematics/college/4jrqhbd4s707uairqkk8nmrp4qqfc6dh9e.png)
cross multiply
![AC^(2) =36](https://img.qammunity.org/2022/formulas/mathematics/college/hy874e5bkslympngzvu0duldshw3ouol4g.png)
take the square root of both sides
AC=6