Review and revise writeups # 1 - 12.
A. Consider any triangle ABC. Select a point P inside the triangle and draw lines AP, BP, and CP extended to their intersections with the opposite sides in points D, E, and F respectively. Explore (AF)(BD)(EC) and (FB)(DC)(EA) for various triangles and locations of P.
B. Conjecture? Prove it! (You may need to draw some parallel lines to produce some similar triangles). Also, it probably helps to consider the ratio
Can the result be generalized (using lines rather than segments to construct D ABC) so that point P can be outside the triangle? Show a working GSP Sketch.
C. Show that when P is in the triangle, the ratio of the areas of D ABC and D DEF is always greater than or equal to 4. When is it equal to 4?
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