In triangle ABC, label X on AB and Y on AC such that AX : XB = CY : YA = 2 : 1. Extend XY and BC up to point Z by a length $u$ beyond $Y, YZ=u $. Find ZB : ZC in terms of $u$.
2026-04-02 11:45:11.1775130311
Geometry (ratio of subdivided length in a triangle)
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This is the Theorem of Menelaus:
(AX/XB)(BZ/ZC)(CY/YA)=1
Replace AX/XB with 2 CY/YA with 2
And you get ZB/ZC= 1/4