Let p be a point on a curve γ on a surface S, and let Π be the tangent plane to S at p. Let μ be the curve obtained by projecting γ orthogonally onto Π . Show that the curvature of the plane curve μ at p is equal up to sign,to the geodesic curvature of γ at p.

I have no idea how to prove this. All i know than is that the normal curvature is given by $\displaystyle Lu'^2$$\displaystyle +2Mu'v'$$\displaystyle +Nv'^2$