Question 959334
find the length of the chord which is at a distance of5cm from in 
center of a circle whose radius is 10cm
<pre>
{{{drawing(400,400,-11,11,-11,11,

circle(0,0,10), line(5,5sqrt(3),5,-5sqrt(3)),locate(1.2,4.4,10),
line(0,0,10,0),line(5,5sqrt(3)), 

locate(5.2,4.4,expr(1/2)x), 
locate(5.2,-3.7,expr(1/2)x),

locate(2.5,0,5)

 )}}}

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,

{{{5^2+(expr(1/2)x)^2=10^2}}}

{{{25+expr(1/4)x^2=100}}}

{{{expr(1/4)x^2=75}}}

Multiply both sides by 4

{{{x^2=300}}}

Taking positive square roots of both sides:

{{{x= sqrt(300)}}}

{{{x= sqrt(100*3)}}}

{{{x= sqrt(100)sqrt(3)}}}

{{{x=10sqrt(3)}}}

That's approximately 17.32050808 cm

Edwin</pre>