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Book III   Proposition 10
Then, since
    in the circle ABC a straight line AC cuts a straight line BH into two equal parts and at right angles,

the center of the circle ABC is on AC. [III.1, Por.]


Again, since
    in the same circle ABC a straight line NO cuts a straight line BG into equal parts and at right angles,

the center of the circle ABC is on NO. [III.1, Por.]
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