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Book IV   Proposition 3
Now, since LM, MN, NL touch the circle ABC at the points A, B, C, and KA, KB, KC have been joined from the center K to the points A, B, C, therefore
    the angles at the points A, B, C are right. [III.18]

And, since the four angles of the quadrilateral AMBK are equal to four right angles, inasmuch as AMBK is in fact divisible into two triangles,
and the angles KAM, AMB are right,
therefore
    the remaining angles AKB, AMB are equal to two right angles.
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