SOLUTION: find the length of the chord which is at a distance of5cm from in center of a circle whose radius is 10cm

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Question 959334: find the length of the chord which is at a distance of5cm from in center of a circle whose radius is 10cm
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
find the length of the chord which is at a distance of5cm from in
center of a circle whose radius is 10cm


Let the length of the chord be x.  Then half x is above the horizontal
radius and half of it below.

By the Pythagorean theorem,

5%5E2%2B%28expr%281%2F2%29x%29%5E2=10%5E2

25%2Bexpr%281%2F4%29x%5E2=100

expr%281%2F4%29x%5E2=75

Multiply both sides by 4

x%5E2=300

Taking positive square roots of both sides:

x=+sqrt%28300%29

x=+sqrt%28100%2A3%29

x=+sqrt%28100%29sqrt%283%29

x=10sqrt%283%29

That's approximately 17.32050808 cm

Edwin