\[\begin{array}{l} {\text{Point }}B{\text{ is the focus of lemniscate }}\rho = \sqrt {\cos 2\varphi } ,{\text{ }}C{\text{ is the point of maximum}}{\text{, }}A\left( {0;0} \right). \hfill \\ {\text{Prove that }}\angle BAC = {30^ \circ }{\text{ and }}AB = AC. \hfill \\ \end{array} \]