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The chord of a circle of radius 6 ft is 8 ft long . find the distance if the chord from the center.​

User Cagreen
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1 Answer

19 votes
19 votes

Referring to attached figure :

given values : -

  • radius of the circle = 6 ft

  • measure of chord = 8 ft (AB)

construction : -

I actually draw a perpendicular on chord from the centre, and we know that the perpendicular from centre on it bisects the given chord, therefore measure of

  • AC = BC = 1/2 × AB

  • AC = BC = 4 ft

now, let's apply Pythagoras theorem for triangle OCB,

we get :

  • OC² + CB² = OB²

  • OC² + 4² = 6²

  • OC² + 16 = 36

  • OC² = 36 - 16

  • OC² = 20

  • OC =
    √(20) ft

  • OC =
    2√(5) ft

And here OC is the distance of chord from its center, therefore required answer is
2√(5)


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The chord of a circle of radius 6 ft is 8 ft long . find the distance if the chord-example-1
User Hitchhiker
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