Answer:
The perimeter of triangle ABC is 30 units.
Step-by-step explanation:
Given information: AC, CB and BA are tangents.
According to the property of tangents from the same external point, the tangent segments to a circle are equal.
Using this property we can say that
![AD=FA=5units](https://tex.z-dn.net/?f=AD%3DFA%3D5units)
![EB=FB=4units](https://tex.z-dn.net/?f=EB%3DFB%3D4units)
![DC=CE=6units](https://tex.z-dn.net/?f=DC%3DCE%3D6units)
The perimeter of triangle ABC is
![perimeter=AC+CB+BA](https://tex.z-dn.net/?f=perimeter%3DAC%2BCB%2BBA)
![perimeter=AD+DC+CE+EB+BF+FA](https://tex.z-dn.net/?f=perimeter%3DAD%2BDC%2BCE%2BEB%2BBF%2BFA)
![perimeter=5+6+6+4+4+5=30](https://tex.z-dn.net/?f=perimeter%3D5%2B6%2B6%2B4%2B4%2B5%3D30)
Therefore the perimeter of triangle ABC is 30 units.