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MathNet 2006 — Part 02 Question 150

Math Olympiad Vault · MathNet 2006 — Part 02

Question 150

Manoel tested his aim by launching five arrows at the reticulated target with squares of length $1~\mathrm{cm}$, illustrated in the figure. An arrow that hits inside the smaller circle counts 300 points; in the shaded region it counts 100 points, between the shaded region and the larger circle it counts 50 points and outside the larger circle it counts nothing. Manoel's arrows hit the spots
$$
A=(1,-1),\ B=\left(\frac{5}{2}, 1\right),\ C=(1,-4),\ D=(-4,-4)\ \text{e}
$$
$E=(6,5)$.
Question illustration


a. Mark on the figure the points where Manoel hit his arrows.


b. How many arrows did he shoot inside the smallest circle?


c. How many points did Manoel score in total?