Advanced High-School Mathematics

SECTION 1.6 Mass Point Geometry 53

From the above, it’s easy to compute the desired ratios:

EF :FD=^95 : 7 = 9 : 35 and BF :FG=^307 :^15835 = 75 : 79.

Exercises

1. In 4 ABC, D is the midpoint of [BC] and E is on [AC] with
   AE:EC = 1 : 2. LetGbe the intersection of segments [BE] and
   [AD] and findAG:GDandBG:GE.


2. In 4 ABC,Dis on [AB] withAD= 3 andDB= 2. E is on [BC]
   iwhtBE= 3 andEC= 4. ComputeEF :FA.


3. In quadrilateralABCD,E, F, G, andHare the trisection points
   of [AB],[BC],[CD], andDAnearerA, C, C,andA, respectively.
   Show that EFGH is a parallogram. (Show that the diagonals
   bisect each other.)


4. Let [AD] be an altitude in 4 ABC, and assume that ∠B = 45◦
   and∠C= 60◦. Assume that F is on [AC] such that [BF] bisects
   ∠B. LetE be the intersection of [AD] and [BF] and compute
   AE:EDandBE:EF.