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  1. MHB Master
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    Last edited by Albert; December 28th, 2013 at 01:07.

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    #2
    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.

  3. MHB Master
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    #3 Thread Author
    Quote Originally Posted by caffeinemachine View Post
    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

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    #4
    Quote Originally Posted by Albert View Post
    very good solution
    Thanks.

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