|Book IV Proposition 2|
Then, since a straight line AH touches the circle ABC, and from the point of contact at A
the straight line AC is drawn across the circle, therefore
the angle HAC is equal to the angle ABC in the alternate segment of the circle. [III.32]
the angle HAC is equal to the angle DEF;
the angle ACB is also equal to the angle DEF.
For the same reason
the angle ACB is also equal to the angle DFE.
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