Question 947424

In a circle with a 12-inch radius, find the length of a segment joining the midpoint of a 20-inch chord and the center of the circle
<pre>Two of the radii of the circle, along with the chord (base segment) form an isosceles triangle.
One of the congruent sides (radius of circle), the segment being sought, and {{{1/2}}} of the 20" base,
or 20" chord, form a right-triangle. Thus we have a right-triangle with hypotenuse: 12, one leg: 10,
and the segment joining the center of the circle, and the midpoint of the chord,  or h.
We then get: {{{h^2 + 10^2 = 12^2}}}
{{{h^2 = 12^2 - 10^2}}}
{{{h^2 = 144 - 100}}}
{{{h^2 = 44}}}
Segment joining the center of the circle, and the midpoint of the chord, or {{{h = sqrt(44)}}}, or {{{h = sqrt(4 * 11)}}}, or {{{highlight_green(h = 2sqrt(11))}}}