Explanation:

Given, Chords AB = 8 cm and CD = 6 cm
Then, AE = EB = 4 cm and CF = FD = 3 cm
EF = 1 cm
Let OE = x cm
Then, OF = (x + 1) cm
OA = OC = r cm     (? radius)
From ΔOAE, By pythagoras theorem
OA² = AE² + OE²
⇒  r² = 4² + x²
⇒  x² = r² – 16     ...(i)
From ΔOCF, By pythagoras theorem
OC² = CF² + OF²
r² = 3² + (x + 1)²
(x + 1)² = r² – 9      ...(ii)
By equation (ii) – (i),
(x + 1)² – x² = r² – 9 – r² + 16
⇒  x² + 1 + 2x – x² = 7
⇒  2x = 7 – 1 = 6
⇒  x = 3 cm
∴  From equation (i),
9 = r² – 16
⇒  r² = 25
⇒  r = 5 cm