SOLUTION: in a circle whose diameter is 20 inches, a chord is 6 inches from the center. what is the length of the cord?

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Question 192963: in a circle whose diameter is 20 inches, a chord is 6 inches from the center. what is the length of the cord?
Found 2 solutions by jim_thompson5910, RAY100:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
First, draw a picture

From the diagram, we see that half of the length of the chord "x" is a leg of a triangle with another leg of 6 units and a hypotenuse of 10 units.

Since we can see that the triangle has legs of 6 and x with a hypotenuse of 10, we can use the Pythagorean theorem to find the unknown side.

Pythagorean theorem:

where a and b are the legs of the triangle and c is the hypotenuse

Plug in a=6, b=x, and c=10. Now lets solve for x

Square each individual term

Subtract 36 from both sides

Combine like terms

Take the square root of both sides. Note: only the positive square root is considered.

Simplify the square root

Since the length of "x" is half of the length of the chord, this means that is the length of the entire chord.

So the length of the chord is 16 units.

Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
a rough sketch might help
from center of circle draw a horizontal line to circle perimeter
about half way out draw a perpendicular chord.
from center to point on circle that chord intersects draw the last line. This is a radius and the length is 10.
the triangle constructed is a right triangle, since it bisects a chord.
let x be distance from center of the circle to intersection of chord. This is given to be 6
pythagorous is a good tool for rt triangles. In our case one leg is 6, and the hypotenuse is 10.
c^2=a^2+b^2
10^2 =6^2 +b^2
100-36=64=b^2
or b=8
chord total length is 2b, or 16