Hints and Answers

1.
$5:11$ 2. $\frac{1}{2}+\frac{1}{1} = \frac{3}{2}$
3.
$\frac{3}{2}$ 4. $1:5$
5.
$5:4$ 6. $3:2$
7.
$1:2$ 8. $5:3:2$
9.
$9:2$ 10. $\frac{\sqrt{3}}{2}$
11.
$\frac{1}{3}+\frac{1}{2} = \frac{5}{6}$ 12. $2:1$
13.
$5:18$
14.
Split $cd(b-a)$ and $ab(d-c)$ at $A$ and assign $cad$ to $B$ and $cab$ to $C$.
15.
315
16.
441 (Show $\frac{d}{a+d}+\frac{d}{b+d}+\frac{d}{c+d}=1$.)
17.
108 (Show CP:PF = 3:1. Draw a line segment from $D$ to the midpoint of $PB$. Notice that it forms a 3-4-5 triangle which is one-eighth of the total area.
18.
94 (Assign weights of $x,y,z$ to the vertices, find the ratios and multiply.)
19.
$2:3$ (First draw $\overline {GC}$ intersecting $\overline{DF}$ at $K$. Find $CK:KG$. Now work on triangle $DCG$.)