A Point on a Segment in a Rhombus

★ 6/10plane geometry Parametrization vectors

Problem

As shown in the figure, $ABCD$ is a rhombus with side length $\sqrt 3$ and $\angle DAB=\dfrac{\pi}3$ . Point $E$ lies on side $CD$ with $DE=\dfrac 12 EC$ , point $F$ is the midpoint of side $BC$ , and $G$ is a point on segment $EF$ such that

\overrightarrow{AG}=\dfrac 12\overrightarrow{AC}+t\,\overrightarrow{AD}

for some real number $t$ . Find the value of $\left|\overrightarrow{BG}\right|$ .

Answer

Solution

Difficulty	6/10
Topics	plane geometry, Parametrization, vectors

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