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Book IV   Proposition 5
And it is manifest that,
    when the center of the circle falls within the triangle,
    the angle BAC, being in a segment greater than the semicircle, is less than a right angle;

    when the center falls on the straight line BC,
    the angle BAC, being in a semicircle, is right;
and
    when the center of the circle falls outside the triangle,
    the angle BAC, being in a segment less than the semicircle, is greater than a right angle. [III.31]
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