Consider a half circle with diameter $AB$.Draw the tangent $Ax$, $By$ with half circle. Take $M$ on $Ax$, $N$ on $By$ such that $AM*BN=R^2$. Prove that the outer circle of the triangle $OMN$ is always tangent to a fixed line.
I will $MN$ is a fixed line and $O;R$ cut $MN$ at OH is a fixed line
I see: $MN=MA+NB$ and $MN^2=MA^2+NB^2+2MA*NB=MA^2+NB^2+2R^2$
So i So I need to prove $MA^2+NB^2$ is a fixed line but i can't. Help me