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Let $A, B, C, D$ and $E$ be five points marked in clockwise order, on the unit circle in the plane (with centre at origin). Let $\alpha$ and $\beta$ be real numbers and set $f(p)=\alpha x+\beta y$ where $P$ is a point whose coordinates are $(x,y)$. Assume that $f(A)=10, f(B)=5, f(C)=4$ and $f(D)=10$. Which of the following are impossible?

a) $f(E)=2$

b) $f(E)=4$

c) $f(E)=5$

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    $\begingroup$ Hint: The line $AD$ split the plane into two components and the point $E$ is lying on different side from the pair $B$ and $C$. Since $f$ is constant along the line $AD$.... $\endgroup$ – achille hui Jan 15 '14 at 14:14
  • $\begingroup$ @achillehui Like to say more on your comment? $\endgroup$ – Mick Jun 22 '14 at 18:29

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