Question 765504
Two parallel chords on opposite sides of the centre of a circle are 9 cm apart. If the chords are 8 cm and 12 cm long, then what is the radius of the circle?
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I don't have the means to draw the sketch, but I can try to describe it to you. I am working with two right triangles. Both triangles have the radius as the hypotenuse with a known leg=1/2 of the length of the respective chords (4 and 6 cm). The sum of the unknown legs=distance(9cm) between the given chords.
r=radius
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{{{sqrt(r^2-4^2)+sqrt(r^2-6^2)=9}}}
{{{sqrt(r^2-4^2)=9-sqrt(r^2-6^2)}}}
square both sides
{{{r^2-16=81-18*sqrt(r^2-36)+r^2-36}}}
{{{18*sqrt(r^2-36)=61}}}
{{{sqrt(r^2-36)=61/18}}}
square both sides again
r^2-36=11.48
r^2=36+11.48=47.48
r=√47.48
r=6.89 cm