52 CHAPTER 1 Advanced Euclidean Geometry
Note that in the above diagram,QP :PR= (b 2 +c) : (a+b 1 ) because
P is the center of mass of [QR].
Example 4. In the figure below, computeEF :FDandBF :FG.
Solution. We shall arrange the masses so that the point F is the
center of mass. So we start by assigning weights toAandBto obtain
a balance [AB] at E: clearly, assigning mass 4 to B and 3 to Awill
accomplish this. Next, to balance [AC] at Gwe need to assign mass
9
7 to C. Finally, to balance [BC] atD, we need another mass of
18
35 at
B, producing a total mass of 4 +^1835 at B. The pointF is now at the
center of mass of the system! See the figure below: