Construct a point n

[Albert]

Construct a point N

 

[caffeinemachine]

Re: Construct a point N

View attachment 1811

Let $r$ be the ray which passes through $M$ and whose beginning point is $B$.

Let $P$ be a point such that $\angle PBA=\angle ABC$.
Draw a ray $l$ which is perpendicular to $AB$ and whose beginning point is $P$.

Let $l$ intersect $BC$ at $N'$.
Let Find a point $M'$ on $r$ such that $|N'M'|=|PN'|$.
Now find a point $N$ on $BC$ such that $\Delta M'BN'\sim MBN$. Then $N$ is the required point.

 

[Albert]

Re: Construct a point N

Let $r$ be the ray which passes through $M$ and whose beginning point is $B$.

Let $P$ be a point such that $\angle PBA=\angle ABC$.
Draw a ray $l$ which is perpendicular to $AB$ and whose beginning point is $P$.

Let $l$ intersect $BC$ at $N'$.
Let Find a point $M'$ on $r$ such that $|N'M'|=|PN'|$.
Now find a point $N$ on $BC$ such that $\Delta M'BN'\sim MBN$. Then $N$ is the required point.

very good solution

 

[caffeinemachine]

Re: Construct a point N

very good solution

Thanks.