# 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 isA. 5 cmB. 6 cmC. 7 cmD. 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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