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

  1. 4 cm

  2. 5 cm

  3. 6 cm

  4. 8 cm

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Answer

The figure is shown below:

At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is (a) 4 cm (b) 5 cm (c) 6 cm (d) 8 cm. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Since tangent and radius at point of contact of a circle are perpendicular to each other. Hence,

XAY ⊥ AO

Given XAY || to CD hence,

CD ⊥ AB.

In right angled triangle OEC,

OE = AE - AO = 8 - 5 = 3 cm.

⇒ OC2 = OE2 + CE2 (By pythagoras theorem)
⇒ 52 = 32 + CE2
⇒ CE2 = 25 - 9
⇒ CE2 = 16
⇒ CE = 4 cm.

Similarly in right angled triangle OED,

⇒ OD2 = OE2 + ED2 (By pythagoras theorem)
⇒ 52 = 32 + ED2
⇒ ED2 = 25 - 9
⇒ ED2 = 16
⇒ ED = 4 cm.

⇒ CD = CE + ED = 4 + 4 = 8 cm.

Hence, Option 4 is the correct option.

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