Additional Practice Problems   
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}