Question

A chord of length 14 cm is at a distance of 6 cm from the centre of a circle. The length
of another chord at a distance of 2 cm from the centre of the circle is

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Answer 1

The length of another chord at a distance of 2 cm from the center of the circle is 18 cm.

Step-by-step explanation:

The diagram for the given situation is shown below.

From the figure, O is the center of the circle. AB is a chord of length 14 cm, CD is the length of another chord, OE is the perpendicular distance from O to AB. OF is the perpendicular distance of CD from O.

Now, from right angled triangle AEO,

$AO^2=OE^2+AE^2\\AO^2=6^2+7^2\\AO^2=36+49\\AO^2=85\\AO=\sqrt{85}$

AO is the radius of the circle. Thus, OC = AO = $\sqrt{85}$ cm

Now, from right angled triangle COF,

$OC^2=OF^2+FC^2\\(\sqrt{85})^2=2^2+FC^2\\85=4+FC^2\\FC^2=85-4\\FC^2=81\\FC=\sqrt{81}=9\ cm$

Now, the chord CD is twice the length of side FC.

Therefore, $CD=2FC=2\times 9=18\ cm$

Answer 2

Answer:

9cm

Step-by-step explanation:

see above

thank you it's correct