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Book I   Proposition 37
Then each of the figures EBCA, DBCF is a parallelogram; and
    they are equal, for they are one the same base BC and in the same parallels BC, EF. [I.35]

Moreover
    the triangle ABC is half of the parallelogram EBCA; for the diameterAB bisects it. [I.34]
And
    the triangle DBC is half of the parallelogram DBCF; for the diameter DC bisects it.
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