Find a point on the edge of a pyramid

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Let $VABCD $ a pyramid such that all the edges are equal. Find $P\in VB $ s.t. $AP+PC $ is minim.

I try to determine the point with the unfolding of pyramid but I didn't succed.

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The shortest paths from $A$ and $C$ to $VB$ are those with $AP$ and $CP$ perpendicular to $VB$. As $ABV$ and $CBV$ are equilateral triangles, that happens when $P$ is the midpoint of $VB$.