T
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E

E
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Book III   Proposition 37
But
    the angle DEF is right;
therefore
    the angle DEF is also right.

And FB produced is a diameter; and
    the straight line drawn at right angles to the diameter of a circle, form its extremity, touches the circle; [III.16, Por.]
therefore
    DB touches the circle.

Similarly this can be proved to be the case even if the center be on AC.

Being what it was required to prove.
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