Question 1156833
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Make a sketch.


Draw the perpendicular radius to the first chord.


Find right angled triangle in the sketch.


For this right angled triangle, write the Pythagorean formula


    r^2 = d^2 + L^2,    (1)


where r is the radius of the circle, d is the distance of the chord from the center of the circle 
and L is half the chord's length.


Then from (1) you get

    r^2 = 2^2 + (6/2)^2 = 4 + 3^2 = 4 + 9 = 13.


Thus the radius of the circle is  {{{sqrt(13)}}}.


Now write equation (1) for the chord, which is 1 cm from the center of the same circle

    13 = 1^2 + (x/2)^2 

where x the length of this chord.


You then get

    (x/2)^2 = 13 - 1 = 12;

    x/2 = {{{sqrt(12)}}} = {{{2*sqrt(3)}}}


<U>ANSWER</U>.  The length of the cord is  {{{4*sqrt(3)}}} = 6.928 centimetres.
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