How to calculate the length of the chord in a circle?.

 Calculating the length of the chord is essential in Civil engineering when you need to find out the cutting length of the rebars in a circular slab.

Now, let us observe the procedure to find out the length of the chord in the below-given circle.

The diameter is said as the largest chord of the circle.

The formula for finding the length of the chord 

 =2√r2 - d2

Given data:

The diameter of circle D = 1500mm

Chord distance from the center of the circle= d = 100mm.

For your understanding, I have redrawn the triangle ecf as below.

Here, 

Chord length = ef 

cf = r = radius of circle 

      = D /2 

  

    r  = 1500mm/2 = 750mm.

The distance of the chord from the center of the circle = d = 100mm.

Chord length ef 

       =2√r2 - d2

      =2√7502 - 1002

      = 2√ 562500 - 10000

= 2 √ 552500

= 2 × 743.303

= 1486.6 mm.

Similarly, you can calculate the length of all other chords by changing the value of d.

Now, let us calculate the length of chord-2 i.e. chord ij  

Chord length ij

       =2√r2 - d12

   Here, 

d1 =100mm+ 100mm

  

    = 200mm   

  Chord length ij

      =2√7502 - 2002

      = 2√ 5,62500 - 40000

= 2 √ 5,22500

= 2 × 722.84

= 1445.68 mm.

To go through the articles on Estimation & calculation in civil engineering, click here.

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