Answer:
r = 5
Step-by-step explanation:
Using Pythagoras' identity in the right triangle ABC
AC² = BC² + AB²
(r + 8)² = r² + 12² ← expand left side using FOIL
r² + 16r + 64 = r² + 144 ( subtract r² from both sides )
16r + 64 = 144 ( subtract 64 from both sides )
16r = 80 ( divide both sides by 16 )
r = 5
