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a straight line AD touches the circle ABE, and from the point of contact at A a straight line AB is drawn across the circle ABE,
the angle DAB is equal to the angle AEB in the alternate segment of the circle. [III.32]
But
the angle DAB is equal to the angle at C;
therefore
the angle at C is also equal to the angle AEB.
Therefore
on the given line segment AB the segment AEB of a circle has been described admitting the angle AEB equal to the given angle, the angle at C.
Being what it was required to do.
