we know that
The incenter is the point equidistant from the triangle's sides
so
that means
CI=BI=AI
substitute the given values
BI=AI
5x-11=3x+7
solve for x
5x-3x=7+11
2x=18
x=9
Find the value of CI
CI=52-2x
substitute teh value of x
CI=52-2(9)
CI=34 units
Verify the values of AI and BI
AI=