MHB Construct Point N: Guide to Building a Project Plan

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The discussion outlines a geometric construction to find point N based on given points and angles. It involves using ray r through point M and point B, and establishing point P such that angle PBA equals angle ABC. A perpendicular ray l from P intersects line BC at point N'. The construction then requires finding point M' on ray r, ensuring the distance from N' to M' equals the distance from P to N'. Finally, point N is determined on line BC such that triangles M'BN' and MBN are similar, completing the construction.
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Re: Construct a point N

Albert said:
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.
 
Re: Construct a point N

caffeinemachine said:
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 (Clapping)
 
Re: Construct a point N

Albert said:
very good solution (Clapping)
Thanks. :)
 
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