For, since E is the centre of the circles BCD, AFG, EA is equal to EF, and ED to EB;
therefore the two sides AE, EB are equal to the two sides FE, ED:
and they contain a common angle, the angle at E;
therefore the base DF is equal to the base AB,
and the triangle DEF is equal to the triangle BEA,
and the remaining angles to the remaining angles; [I. 4
therefore the angle EDF is equal to the angle EBA.
But the angle EDF is right; therefore the angle EBA is also right.
Now EB is a radius;
and the straight line drawn at right angles to the diameter of a circle, from its extremity, touches the circle; [III. 16, Por.]
therefore AB touches the circle BCD.
Complete text
Book I