Q. 24.1( 40 Votes )

# 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 :

Given that diameter = 26cm

Radius = Diameter / 2 = 26 /2 = 13cm

So, OA = 13cm

And AB = 24 cm

We know that a perpendicular drawn from the center of a circle on its chord bisects

the chord.

∴ AP = PB = 12 cm

In the right angled ΔOAP using Pythagoras theorem,

⇒ OA^{2} = OP^{2} + AP^{2}

⇒ 13^{2} = OP^{2} + 12^{2}

⇒ 169 = OP^{2} + 144

⇒ OP^{2} = 25

⇒ OP = 5cm

So, the distance of chord from the center is 5cm.

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