Question

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

Answer 1

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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