Property: In every triangle the median is divided by the centroid (intersection point of the medians) in a 2:1 ratio, the shorter toward the midpoint of the side. We use this property in all of the above:
1. PD = 15. Since we know CP=30, PD is half of that, i.e., 15
2. FP = 13. Since BF = 39, and we know that FP is 1/3 of BF (see property stated above), FP = 13.
3. BP = 26. Following (2), BF is partitioned by FP and BP as 1:2. Hence BP is 2/3 of FP, or 26.
4. CD=45. In (1) we calculated PD=15 and we are given CP=30, so CD=45.
5. PA=36. We are given EP=18, which is 1/3 of length EA, so PA = 2*EP = 36.
6. EA=54. EA=EP+PA = 18+36=54
