Answer is D. 8 cm
Given:
Radius = OP = 5 cm
Distance of AB and XY = 8 cm
∵ Distance of AB and XY = 8 cm
And AB is parallel to XY
∴ PR = 8 cm
Join OB
Now,
OB = OP = 5 cm [radius]
Also,
OR = PR – PO
⇒ OR = 8 cm – 5 cm
⇒ OR = 3 cm
∴ By Pythagoras theorem in ∆ORB,
OB2 = OR2 + RB2
⇒ 52 = 32 + RB2
⇒ RB2 = 52 – 32
⇒ RB2 = 25 – 9
⇒ RB2 = 16
⇒ RB = 4
Now,
AB = AR + RB
⇒ AB = 2RB
⇒ AB = 2 × 4
⇒ AB = 8 cm
Hence, Length of chord = 8 cm