20sep13

\begin{document}
\maketitle

Tondeur's text does not have many easy, practice problems, similar
to what you can expect on quizzes and tests. So here is a growing
collection of problems to test your understanding of the material.

You should also treat these problems as a practice quiz, so write your answers on scratch
paper. Check your answers to the  solutions . Then put them
into your journal for future reference.

\begin{enumerate}
\item
In the barycentric coordinates $(a,b,c)$ relative to $\triangle ABC$
where does the line $a = 0.3$ cross $(AB)$ ?
\item
Given $\triangle ABC$ with $(A'BC), (AB'C), (ABC')$.
Let $A' = -B +2C$ and $B'= 0.5 A + 0.5 C$ find $C'(AB)$ so that the three
cevians are concurrent.
\item
Consider barycentric coordinates $(a,b,c)$ relative to $\triangle ABC$.
Where does the line with equation $2b - c =0$ cross $(BC)$ ?

\item
Given four points $P_1, P_2, P_3, P_4$ with $(P_1 P_2 P_3)$ and  $(P_2 P_3 P_4)$,
show that
$\frac{P_1-P_2}{P_1-P_3} = \frac{P_4-P_2}{P_4-P_3}$  if and only if $P_1=P_4$.
\end{enumerate}

\end{document}