Question 174
From a point $O$ lying outside the line $d$, draw the projection $A$ of $O$ onto $d$. Take some point $M$ on $d$ different from $A$ and $H$ is the projection of $A$ onto $OM$. Denote $D$ as the midpoint of $HM$ and take $N$ on $OA$ such that $NH \perp AD$. Suppose that two circumcircles of triangles $HMN$ and $OAH$ are tangent, calculate the ratio $AM/ AO$.