Question

Diameter of a circle is 30 cm. If the length of a chord is 20 cm, find the distance of the
chord from the centre.​

Answer 1

Answer:

• Distance of the chord from the centre (OE) = 5√5 cm.

Step-by-step explanation:

Diagram:

• Refers to attachment.

Given:

• Diameter of circle (AB) = 30 cm
• Radius of circle (AO) = 15 cm
• Length of chord (CD) = 20 cm

To find:

• Distance of the  chord from the centre (OE).​

Construction:

• Draw a ⊥ bisector of chord CD from centre.

∴ CE = DE = 10 cm

And, CO = 15 cm                     (∴ Radius of circle)

Now, by Pythagoras theorem:

In ΔCOE

⇒ CO² = OE² + CE²

⇒ OE² = CO² - CE²

⇒ OE² = 15² - 10²

⇒ OE² = 225 - 100

⇒ OE² = 125

⇒ OE = √125

⇒ OE = 5√5 cm.

Hence, Distance of the chord from the centre (OE) = 5√5 cm.

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