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A circle passes through A and B, and is tangent to line CD. Find its area, in cm^2.
Diagram: https://imgur.com/a/XwWg5Kc
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The problem does not tell it, by it is clear from the plot,
and I will assume it, that AB is parallel to CD.
Make a sketch for better understanding.
Let "r" be the radius of the circle, in centimeters.
The center of the circle lies on the perpendicular bisector to AB,
and the distance from the center to AB is = cm.
Therefore, this equlation is hold
r + = 10 cm
Our task is to solve it to determine the rasdius r.
It is easy. Move r from left side to right
= 10-r.
Square both sides
=
=
Cancel in both sides and simplify
20r = 100 + 4
20r = 104
r = = cm = 5.2 cm.
Now the area of the circle is
= = 266.8741 cm^2 (rounded). ANSWER
Solved.