# SAT1000 - P877

Geometry Level pending

Here's the definition of harmonically bisect: Given that $A_1, A_2, A_3, A_4$ are four distinct points on the coordinate plane, if $\overrightarrow{A_1A_3}=\lambda \overrightarrow{A_1A_2}$, $\overrightarrow{A_1A_4}=\mu \overrightarrow{A_1A_2}$, $\dfrac{1}{\lambda}+\dfrac{1}{\mu}=2$, then $A_3, A_4$ harmonically bisect $A_1, A_2$.

Given that $C(c,0), D(d,0)\ (c,d \in \mathbb R)$ harmonically bisect $A(0,0), B(1,0)$, which choice is true?

$A.\ \textup{C could be the midpoint of AB.}$

$B.\ \textup{D could be the midpoint of AB.}$

$C.\ \textup{C, D could be both on segment AB.}$

$D.\ \textup{C, D can't be both on the extension line of AB.}$

Have a look at my problem set: SAT 1000 problems

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