<PRE><B>Question 1189759</B>
&lt;br&gt;
With an area of 1369ℼ, the radius of the circle is 37.&lt;br&gt;
Let O be the center of the circle; let E be the point where the segment with length y in the diagram intersects CD; and let F be the point of tangency of the circle with line CD.  Draw the diameter FG, intersecting AB at H.&lt;br&gt;
The diameter FG is the perpendicular bisector of chord AB, so the length of GB is x/2.  The given information {{{x/y=1/3}}} then tells us that EB/GB=6.  So&lt;br&gt;
Let GB = w
Then BE = 6w&lt;br&gt;
Draw radius OB and look at right triangle OHB.&lt;br&gt;
{{{(OH)^2+w^2=37^2}}}
{{{OH=sqrt(1369-w^2)}}}&lt;br&gt;
Then we can see FH=EB=6w, so&lt;br&gt;
{{{37+sqrt(1369-w^2)=6w}}}
{{{sqrt(1369-w^2)=6w-37}}}
{{{1369-w^2=(6w-37)^2}}}
{{{1369-w^2=36w^2-444x+1369}}}
{{{37w^2-444w=0}}}
{{{37w(w-12)=0}}}
{{{w=12}}}&lt;br&gt;
y is the length of EB, which is 6w = 72.&lt;br&gt;
ANSWER: y = 72 cm&lt;br&gt;
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