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The point $B$ is on arc $AC = 90$, with center $O$.

$AB/BC= \frac 12$

Express vector $\overrightarrow {OC}$ with vectors $\overrightarrow {OA}$ and $\overrightarrow {OB}$

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Is $AB/BC= \frac 12$ in angular measure or straight line distances?. Pesumably $AC=90$ means $90^\circ$, correct? – Ross Millikan Apr 11 '13 at 21:00
AB/BC=1/2 in arc length – Ubavic Apr 11 '13 at 21:04
up vote 1 down vote accepted

Hint: Let $O$ be the origin, $A$ be $(1,0)$, $C$ be $(0,1)$. Where is $B$? Then write $\vec{OC}=a\vec{OA}+b\vec{OB}$ and you have two equations in two unknowns.

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This problem would be more interesting had $AB$ etc been straight line distances. – Ron Gordon Apr 11 '13 at 21:08

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