Question 551319
Connect the end points of the chord to the center of the circle then draw the angle bisector from the center perpendicular to the chord thus bisecting the chord.
You now have two congruent right triangles in which the hypotenuse is the radius of the circle (10 inches), and whose height is 6 inches.
Using the Pythagorean theorem: {{{c^2 = a^2+b^2}}} where c = 10, a = 6, and b = half the length of the chord.
{{{10^2 = 6^2+b^2}}}
{{{b = sqrt(100-36)}}}
{{{b = sqrt(64)}}}
{{{b = 8}}}
The chord is 2(8) = 16 inches.