Question 1151255
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I'll let you draw the diagram, since I don't know how to include one with my response.<br>
Since the circle passes through A and B, the center of the circle lies on the perpendicular bisector of AB.<br>
Sketch the circle with center O passing through A and B, tangent to CD at E.<br>
Let F be the midpoint of AB, and draw segment EF, which is part of the perpendicular bisector of AB.  Note that the given information tells us the length of EF is 10.<br>
Draw segment OB; then OFB is a right triangle.<br>
Let r be the radius of the circle.<br>
Segment EF, with length 10, is the sum of segments OE and OF.  OE is a radius with length r; and OF is a leg of a right triangle with hypotenuse r and other leg 2.<br>
Then....<br>
{{{10 = r + sqrt(r^2-2^2)}}}
{{{10 = r+sqrt(r^2-4)}}}
{{{10-r = sqrt(r^2-4)}}}
{{{(10-r)^2 = r^2-4}}}
{{{100-20r+r^2 = r^2-4}}}
{{{100-20r = -4}}}
{{{104 = 20r}}}
{{{r = 104/20 = 5.2}}}<br>
The radius of the circle is 5.2.  Use that in the formula for the area of a circle and express the answer in the required form.<br>