Circles A, B, and C are externally tangent to each other. If AB = 14, BC = 18, and AC = 28, then find the radii of each of the circles.
+876 Picture: https://ibb.co/rMsSd3h
Let $a, b, c$ be the radii of $A, B, C$ respectively.
We have: \(\begin{align*} a+b&=14\\ b+c&=18\\ a+c&=16 \end{align*}\)
Add all equations: $2(a+b+c)=48$
Thus: $a+b+c=24$
Subtract $a+b=14, b+c=18, a+c=16$ from $a+b+c=24$ and you will get $c=10, a=6, b=8$
Thus $(a,b,c) = (6,8,10)$
Interesting how this is the length of a Pythagorean triple... probably a coincidence
