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#chord-length
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#geometry
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#circle
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A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of the chord.?

Jan 13

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Jan 13

To find the length of the chord, we can use the Pythagorean theorem.

Let's call the radius of the circle r and the distance from the center of the circle to the chord d.

We know that the diameter of the circle is 26 cm, so the radius is half of that, which is 26/2 = 13 cm.

We also know that the distance from the center of the circle to the chord is 5 cm.

Using the Pythagorean theorem, we can set up the equation:

r^2 = d^2 + (chord length/2)^2

Plugging in the values we know:

(13 cm)^2 = (5 cm)^2 + (chord length/2)^2

169 cm^2 = 25 cm^2 + (chord length/2)^2

144 cm^2 = (chord length/2)^2

Taking the square root of both sides:

12 cm = chord length/2

Multiplying both sides by 2:

24 cm = chord length

Therefore, the length of the chord is 24 cm.

Let's call the radius of the circle r and the distance from the center of the circle to the chord d.

We know that the diameter of the circle is 26 cm, so the radius is half of that, which is 26/2 = 13 cm.

We also know that the distance from the center of the circle to the chord is 5 cm.

Using the Pythagorean theorem, we can set up the equation:

r^2 = d^2 + (chord length/2)^2

Plugging in the values we know:

(13 cm)^2 = (5 cm)^2 + (chord length/2)^2

169 cm^2 = 25 cm^2 + (chord length/2)^2

144 cm^2 = (chord length/2)^2

Taking the square root of both sides:

12 cm = chord length/2

Multiplying both sides by 2:

24 cm = chord length

Therefore, the length of the chord is 24 cm.