Answer:
B. 6/7
Explanation:
You want the radius of each of two circles tangent to each other and the extended segments of ∆ABC.
Proportion
Referring to the attached figure, we see that ∆EGF is similar to ∆ABC. This means EG/EF = AB/AC = 5/4.
∆AGH is also similar to ∆ABC, so we also have the proportion ...
GH/AH = BC/AC = 3/4
In terms of radius r, GH = (3+5/4)r, and AH = r +4:
(17/4)r / (r +4) = 3/4
17r = 3(r +4) . . . . . . . . multiply by 4(r+4)
14r = 12 . . . . . . . . subtract 3r
r = 6/7 . . . . . . divide by 14, simplify
The radius of each circle is 6/7 units.