# Construct a point n

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#### caffeinemachine

##### Well-known member
MHB Math Scholar
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.

#### Albert

##### Well-known member
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

##### Well-known member
MHB Math Scholar
Re: Construct a point N

very good solution Thanks. 