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

Question

Philoid · Accepted 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