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Math · Geometry
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In figure 4.5, compute each of the ratios XP/PY and BQ/QC in terms of the lengths r AX, s EXB and t AY, and u YC. Show that the only way these ratios can be equal is if both ratios equal 1, and show that in that case, XY is parallel to BC. HINT: There are two ways to see concurrent Cevians in Figure 4.5 There are three concurrent interior Cevians for 4ABC, but there are also three concurrent Cevians for 4AXY.

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