Question

At point A on a diameter AB of a circle of radius 10cm, tangent XAY is drawn in the circle. The
length of the chord CD parallel to XY at a distance 16cm from A is

Answer 1

At point A on a diameter AB of a circle of radius 10 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY at a distance 16 cm from A is 16 cm

Step-by-step explanation:

In the given figure

XY is the tangent to the circle

We know that tangent is at right angle with the line joining the tangent point to the centre of the circle

Therefore,

∠OAY = 90°

∵ CD is parallel to XY

Therefore,

∠OAY = ∠BED = 90° (Corresponding angles)

Again,

Given that

AE = 16 cm

And the radius of the circle is 10 cm

Therefore,

AO = 10 cm

∴ OE = AE - AO = 16 - 10 = 6 cm

Also,

OC = 10 cm (Radius of the circle)

In Δ OCE

$OC^2=OE^2+EC^2$

$\implies EC^2=OC^2-OE^2$

$\implies EC^2=10^2-6^2$

$\implies EC^2=100-36$

$\implies EC^2=64$

$\implies EC=\sqrt{64}$

$\implies EC=8 cm$

Therefore,

CD = 2CE  (The perpendicular drawn from the centre of a circle on a chord, bisects it)

$\implies CD=2\times 8$

$\implies CD=16 cm$

Know More:

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Answer 2

Step-by-step explanation:

answer of this question is 16cm