  We utilize the Legendre-Fenchel transform and weak geodesics for
plurisubharmonic functions to construct a weight function that can be used in
the Berndtsson-Lempert method, to give an Ohsawa-Takegoshi extension type of
result. Theorem 4.1 and Theorem 0.1 in \cite{OT2017} (Theorem \ref{Theorem A}
and \ref{Theorem B} below) follow as two special cases of this result, thus
answering affirmatively a question posed by Ohsawa in remark 4.1 in
\cite{OT2017}, on the Berndtsson-Lempert method.
