Question

Find the length of a chord AB which is at a distance of 6 cm from the centre O of a circle

of radius 10 cm.


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Answer 1

⠀⠀⠀☆ Referred to the figure

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Let: AB be the required chord of the circle.

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We have

• Distance from centre (OC) = 6cm
• Radius (OA) = 10cm

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As we can see tha ∆OAC is a right angled triangle. [By using Pythagoras theorem]

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★ OA² = OC² + AC²

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→ (10)² = (6)² + AC²

→ 100 = 36 + AC²

→ AC² = 100 - 36

→ AC² = 64

→ AC = √64

→ AC = 8

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Since, OC is a perpendicular bisector of the chord (AB). So, we can write AB = 2AC

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→ AB = 2 × 8

• → AB = 16cm

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Hence,

• Length of the chord is 16cm.