Now, since the circles ABC, DEF are equal,
the radii are equal.
Thus the two straight lines BG, GC are equal to the two straight lines EH, HF;
and the angle at G is equal to the angle at H;
therefore the base BC is equal to the base EF. [I. 4]
And, since the angle at A is equal to the angle at D,
the segment BAC is similar to the segment EDF; [III. Def. 11]
and they are upon equal straight lines.
But similar segments of circles on equal straight lines are equal to one another; [III. 24]
therefore the segment BAC is equal to EDF.
But the whole circle ABC is also equal to the whole circle DEF;
therefore the circumference BKC which remains is equal to the circumference ELF.