T H E E L E M E N T S	Book IV   Proposition 4
	For, if it cuts them, the straight line drawn at right angles to the diameter of the circle from its extremity will be found to fall within the circle: which was proved absurd; [III.16]     therefore the circle described with center D and distance one of the straight lines DE, DF, DG will not cut the straight lines AB, BC, CA;     therefore it will touch them, and will be the circle inscribed in the triangle ABC. [IV. Def.5]
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