Question 1153751

{{{CD=17m}}}

{{{CD}}} is perpendicular to the chord {{{AB}}}

{{{EC=8m }}}

first sketch it:

{{{drawing ( 600, 600, -25,25, -25, 25,
circle(0,0,17),circle(0,0,.4),circle(0,-8,.4),locate(.5,1.5,C), locate(0.5,-8,E),green(line(-16,-8,16,-8)),locate(-15.5,-8.3,A), locate(15.5,-8.3,B),green(line(-15.3,-8,0,0)),green(line(15.3,-8,0,0)),
locate(1,-3,8m), locate(9,-3,17m),locate(5,-8.5,AB/2),  
graph( 600, 600, -25,25, -25, 25, 0)) }}} 


from right triangle {{{CEB}}}, using Pythagorean theorem, we have

{{{(AB/2)^2=(17m)^2-(8m)^2}}}

{{{(AB/2)^2=289m^2-64m^2}}}

{{{(AB/2)^2=225m^2}}}

{{{AB/2=sqrt(225m^2)}}}

{{{AB/2=15m}}}

{{{AB=15m*2}}}

{{{AB=30m}}}

the length of the chord {{{AB}}} is {{{30m}}}