|Book III Proposition 19|
For suppose it is not, but, if possible,
let F be the center,
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]
the angle FCE is right.
The angle ACE is also right;
the angle FCE is equal to the angle ACE,
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