Three circles centered at A, B, and C touch each other externally. If AB = 8 cm, BC = 5 cm, and AC = 7 cm, calculate the radii of the circles centered at A, B, and C.

Explanation

Since the circles touch externally:
rA + rB = 8, rB + rC = 5, rA + rC = 7.
Adding the first and third equations and subtracting the second gives 2rA = 10, so rA = 5. Then rB = 3 and rC = 2.