cevian ratio explain

Arthur Lee
This figure explains how the ratio YQ:QB can be derived by considering 2 pairs of similar triangles when a point D is added on AX so that YD is parallel to CB. We can see that YQ:QB is close to CX:XB when Y is close to C. The factor AY:AC tells how this ratio CX:XB should be adjusted to give YQ:QB. This relation among the ratios may be helpful in recognising how other cevians are cut in a similar way.