Answer:
The perimeter of triangle ABC is 146 units
Step-by-step explanation:
we know that
The segment AB, AC and BE are tangent to the circle G
so
The circle G is an inscribed circle
The point G is the incenter of the inscribed circle within the triangle
therefore
AE=AD
BF=BE
CD=CF
we have
AB=56 units
BE=16 units
CD=17 units
Find the value of AE
AE=AB-BE
substitute the given values
AE=56-16=40 units
Find the perimeter
The perimeter of triangle ABC is
P=2[AE+BE+CD]
substitute
P=2[40+16+17]=146 units
