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.

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