You can put this solution on YOUR website! Draw this.
The triangle formed by the line from the center to the chord. (perpendicular bisector) is 2 and the other leg (half the chord's length) is 3. The radius is the hypotenuse and is sqrt(13) cm.
The other chord has leg 1 and hypotenuse sqrt(13)
so the other leg , half the chord, is sqrt (12) or 2 sqrt(3)
Length of the chord is 4 sqrt(3) cm.
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 .
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 = = ANSWER. The length of the cord is = 6.928 centimetres.
