Q. 183.8( 4 Votes )

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

Answer :

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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