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Book III   Proposition 32
Then, since a straight line EF touches the circle ABCD at B, and BA has been drawn from the point of contact at right angles to the tangent,
    the center of the circle ABCD is on BA. [III.19]

Therefore BA is a diameter of the circle ABCD; therefore
    the angle ADB, being an angle in a semicircle, is right. [III.31]
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