Mathematics

Calculate the length of a chord which is at a distance 6 cm from the center of a circle of diameter 20 cm.

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Diameter = 20 cm,

∴ Radius = $\dfrac{\text{Diameter}}{2}$ = 10 cm.

From figure,

AB is the chord which is at a distance 6 cm so,

OC = 6 cm and OA = radius = 10 cm.

In right angle triangle OAC,

⇒ OA² = OC² + AC² (By pythagoras theorem)

⇒ 10² = 6² + AC²

⇒ AC² = 10² - 6²

⇒ AC² = 100 - 36 = 64

⇒ AC = $\sqrt{64}$ = 8 cm.

Since, the perpendicular to a chord from the centre of the circle bisects the chord,

∴ CB = AC = 8 cm.

AB = AC + CB = 8 + 8 = 16 cm.

Hence, length of chord = 16 cm.

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