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S		 Book III   Proposition 34
Then, since a straight line EF touches the circle ABC, and BC has been drawn across from the point of contact at B,
    the angle FBC is equal to the angle constructed in the alternate segment BAC. [III.32]
But
    the angle FBC is equal to the angle at D;
therefore
    the angle in the segment BAC is equal to the angle at D.

Therefore
    from the given circle ABC the segment BAC has been cut off admitting an angle equal to the given rectilineal angle, the angle at D.

Being what it was required to do.
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