Synge inequality

Question

Let $f : M \rightarrow N$ be an isometric immersion, and let $\gamma :[0,1] \rightarrow M$ be a smooth curve such that $f\circ\gamma $ is a geodesic in $N$ . Show that $ \gamma$ is a geodesic in M and, for each plane $ \sigma \subset T_{\gamma (t)}M$ such that $\gamma ^{'}(t) \in \sigma$, prove the Synge inequality $K(\sigma ) ≤ \tilde K(\sigma).$ I am very confused because the first part is very easy with the properties of $ f$, but the Synge inequality i don't know how do it. *Upgrade, i think that i have to use this result from the Gauss equation: For an isometric immersion between Riemannian manifolds $f : M^{n }\rightarrow N^{n+p}$, the Gauss equation says that the (sectional) extrinsic curvature of $M^{n}$ in $N^{n+p}$ at $x \in M^{n}$ for a plane $ \sigma \subset T_{x}M$, $Kf(\sigma ) := KM(\sigma )−KN(\sigma )$, is given by $Kf(\sigma ) = <a(X,X),a(Y,Y)> − ||a(X,Y)||^{2} $, where a is the second fundamental form of the immersion and ${X,Y}$ any orthonormal basis of $\sigma$.