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The radius of a circle is 15 cm and the length of one chord of the circle is 20 cm. What is the distance of the chord from the centre of the circle?

The radius of a circle is 15 cm and the length of one chord of the circle is 20 cm. What is the distance of the chord from the centre of the circle? Correct Answer 5√5 cm

Given:

The radius of the circle = 15 cm

The length of one chord of the circle = 20 cm

Formula Used:

(OC)2 = (OA)2 – (CA)2

Where OC → Distance of the chord from the centre of the circle

OA → Radius of the circle

CA → (1/2) × length of the chord

Calculation:

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In the given figure,

AB = 20 cm

CA = (1/2) × AB

⇒ (1/2) × 20

⇒ 10 cm

OA = radius = 15 cm

(OC)2 = (OA)2 – (CA)2

⇒ (OC)2 = 152 – 102

⇒ (OC)2 = 225 – 100

⇒ OC = √125

⇒ OC = 5√5 cm

∴ The distance of the chord from the centre of the circle is 5√5 cm.  

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