Question 739872
Draw a picture. The distance between the chord and the circle's center is measured at the chord's midpoint (draw this in) and then connect the chord's endpoints with the circle's center -- these are radii.

You should see two mirror-image right triangles.

here is a picture:


{{{drawing( 600,600, -15, 15, -15, 15, 
         grid(0),blue( circle( 0, 0, 10 ) ),blue(line( 0, 6, 0, 0 )),green(line( 8, 6, 0, 0 )),green(line( -8, 6, 0, 0 )),green(line( -14, 6, 14, 6 )),locate( -8, 6, A ),locate( 8, 6, B ),locate( 0.1, 6.4, C ),locate( 0.1, -0.3, O ),locate(4,6.5,8cm),locate(-4,6.5,8cm),locate(0.2,3.3,6cm)
         
)}}}


 You have enough information to know the two legs of each triangle, and its hypotenuse is the circle's radius, which you can find using the Pythagorean theorem.

{{{r^2=8^2+6^2}}}

{{{r^2=64+36}}}

{{{r^2=100}}}

{{{r=sqrt(100)}}}

{{{r=10}}}