2019 · Q30
Let the bisector of the ∠BAC of △ABC meet BC in X. Which one of the following is correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AAB < BX
- BAB > BX
- CAX = CX
- DNone of the above
Explanation
Let angle BAC = 2.alpha, bisected into alpha each. In triangle ABX, side AB is opposite angle AXB = 180-B-alpha, and side BX is opposite angle alpha. Since A+B < 180, 180-B-alpha > alpha, so AB > BX.