Question

Diameter of a circle is 26 CM. and length of a chord of the circle is 24 CM. Find the distance of the chord from the center.

Answer 1

Hello friend

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First Draw a Circle with center O and chord AB and give name M in the middle of seg AM and join the lines as shown in the figure which I will upload in the answer..okk

Now,lets write all the given values

So, O is the center of the circle

Seg OM is perpendicular seg AB

Seg AB = 24 cm

Diameter of the circle = 26 cm.

And Seg OM = ??

We know that,

radius = diameter/2

radius = 26/2

radius = 13 cm.

: AO = 13 cm.


: AB = AM + MB

24 = 2AM

AM = 24/2

AM = 12 cm .

Now,In triangle OMA

angle OMA = 90°

Seg AO = 13 cm

Seg AM = 12 cm.

Seg OM = ??

By using the Pythagoras theorem,

(hypotenuse)^2 = (one side)^2 +(second sides)^2

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

(13)^2 = (12)^2 + (OM)^2

169 = 144 + (OM)^2

(OM)^2 = 169 - 144

(OM)^2 = 25

OM = 5 cm ..........(taking square root)

Therefore, the distance of the chord from the center is 5 cm