Arcs, Cevians, Tangents Theorem 4.5 The lines tangent to the
circumcircle of a triangle at its vertices cut the opposite
sides in three collinear points. The proof in the text is as
follows: Let the tangent to the circumcircle at A meet line BC
at L. Then Angle BAL is congruent to angle C since each angle is
measured by half of arc AB. *****That would be fine, but I don't
know how they determine this... *****. Also we have that angle
LAC = 180 - angle ABC, since these angles are measured by halves
of the two opposite arcs AC. *****Again, I am lacking the
theorem which is used to deduce this******.... the rest of the
proof is trivial and I don't need help with it. Can someone
please give me the theorems they use for those parts of the
proof. Uploaded with ImageShack.us It's elementary theorem that
angles on the circumference of the circle 'looking' at the same
arc of that circle are themselves equal. (the proof is a bit
long but if necessary I can try to write it, try this
Circumferential Angle Is Half Corresp