|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]
the angle FBC is equal to the angle at D;
the angle in the segment BAC is equal to the angle at D.
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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