Mathematics

A chord of length 8 cm is at a distance 3 cm from the centre of the circle. Calculate the radius of the circle.

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From figure,

AB is the chord which is at a distance 3 cm from the center so OC = 3 cm.

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

∴ CB = AC = $\dfrac{8}{2}$ = 4 cm.

In right angle triangle OAC,

⇒ OA² = OC² + AC² (By pythagoras theorem)

⇒ OA² = 3² + 4²

⇒ OA² = 9 + 16

⇒ OA² = 25

⇒ OA = $\sqrt{25}$ = 5 cm.

Hence, radius = 5 cm.

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