Question

AB and CD are two parallel tangent. To a circle of radius 5cm. The diatance between the tangent is.

Answer 1

Step-by-step explanation:

A chord CD is drawn which is parallel to XY and at a distance of 8cm from A.

As we know that tangent at any point of a circle is perpendicular to the radius through the point of contact.

∴∠OAY=90°

As sum of cointerior angle is 180°.

Therefore,

∠OAY+∠OED=180°

⇒∠OED=90°

AE=8cm(From fig.)

Now in △OEC, by pythagoras theorem,

OC2=OE2+EC2

⇒EC2=OC2−OE2

⇒EC2=(5)2−(3)2

⇒EC=25−9=4

Therefore,

Length of chord CD=2×CE(∵perpendicular from centre to the chord bisects the chord)

⇒CD=2×4=8cm

Hence the length of the chord CD is 8cm.