Question

Distasance of chord AB from the center of a circle is 8 CM.Lenght of the chord AB is 12 CM. Find the diameter of the circle.

Answer 1

Hello friend

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Draw a Circle with center O and chord AM .

Now join the AO and OM as shown in the figure above..

Let's write all the given values.

O is the center of the circle

Seg OM = 8 cm.

Seg AB = 12 cm

Diameter of the circle= ??

: AB = AM + MB

12 = 2AM

AM = 12/2

AM = 6 cm.

Now,

In triangle OMA

angle OMA = 90°

Seg OM = 8 cm

seg AM = 6 cm

So,we have to find it's diameter means first we have to it's radius means AO.

Hence,

By using Pythagoras theorem,

(AO)^2 = (AM)^2 + (OM)^2

(AO)^2 = (6)^2 + (8)^2

(AO)^2 = 36 + 64

(AO)^2 = 100

AO = 10 ..........(taking square root)

: AO = 10cm.

Means radius is 10 cm.

We know that,

Diameter = 2 x radius

Diameter = 2 x 10

Diameter = 20 cm.

Therefore, the diameter of the circle is 20cm.

Thanks.

:)