= Solution
Let $R$ be reflection in the plane. Choose a point of the regular intersection curve and a <unit tangent vector> $w$ to it. Both the point and $w$ are fixed by $R$. The unique local <geodesic> with these initial data is carried by the <surface> <isometry> $R$ to another <geodesic> with the same initial data. Uniqueness therefore gives $R\gamma=\gamma$. Its image lies in the fixed-point set of the reflection, namely the plane, hence locally in the intersection curve. Thus \b[the intersection curve is a <geodesic>], when parametrized by arclength.
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