Point 7 of 9 — Unit 3: Parallel Lines, Proportional Segments and Angle BisectorsQuestion bank: 0 questions (0 with pictures)
073-7 The external bisector theorem
The bisector of theexteriorangle at A meets theextensionof BC at a point E such thatBE/EC = AB/AC, with E outside the segment BC, on the side of the shorter adjacent side.
If AB = AC the external bisector isparallel to BC, so it never meets the line BC and there is no external division point.
Converse: verify that E lies on the extension of BC (outside the segment) andthat BE/EC = AB/AC; then AE is the external bisector.
The internal and external bisectors at the same vertex are perpendicular to each other, so D and E subtend a right angle at A; B, D, C, E form a harmonic range with AB/AC.
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