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At one end of a diameter PQ of a circle of radius 5 cm, tangent XPY is drawn to the circle. The length of chord AB parallel to XY and at a distance of 8 cm from P is

A. 5 cm 

B. 6 cm 

C. 7 cm 

D. 8 cm

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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

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