In the figure, the three segments are tangent to the circle at points b, f, and g. if y=2/3x, find x, y, and z.

We know that

y=(2/3)x
in the tangent at the circle at the point G
x+y=45 in> x+(2/3)x=45> (5/3)x=45> x=45*3/5> x=27 in
y=45-x> y=45-27> y=18 in

in the tangent at the circle at the point B
z+y=39
z=39-y> z=39-18> z=21 in

in the tangent at the circle at the point F
z+x=48
so
21+27=48
so
48=48> is ok

the answer is
x=27 in
y=18 in
z=21 in