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Book III   Proposition 19
For suppose it is not, but, if possible,
    let F be the center,
and
    let CF be joined.

Since a straight line DE touches the circle ABC, and FC has been joined from the center to the point of contact,
    FC is perpendicular to DE; [III.18]
therefore
    the angle FCE is right.
But
    The angle ACE is also right;
therefore
    the angle FCE is equal to the angle ACE,
the less to the greater: which is impossible.
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