# In a circle , a chord 3 centimeters away from the center is 8 centimeters long . how long is a chord ,1.4 centimeters away from the center in the circle ?

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Join OA. Then Triangle ACO have sides 4cm, 3cm and radius r. Then Radius = √(4² + 3²) = 5.

Now draw a chord 1.4cm from centre O. Let this chord meet circle at points D, E.

Let perpendicular 1.4cm long meet chord DE at F. Join OD which is = radius = 5.

Now in triangle ODF, OD = 5, OF = 1.4 . Hence DF = √(OD² - OF²) = √(5² - 1.4²) = 4.8. Hence length of the chord = 2x4.8 = 9.6cm

Complete triangle

AB = 8 cm

Since OM bisects AB

Therefore, AM = BM = 4 cm

In the right triangle OMA

OM = 3 cm, AM = 4 cm

Therefore, by Pythagorean theorem, OA = 5 cm

That is, the radius of the circle = 5 cm

Now, ON = 1.4 cm

Let CN = x cm

By pythagorean theorem

x = 4.8

Therefore, the length of the chord CD = 2x = 9.6 cm