Question

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.

Answer 1

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