<ALB=60^o wanted if AN/CN = AL/CL > 1, AB=BC

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#1 h Nov 19, 2021, 4:53 AM

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The point $L$ is the internal point of the side $AC$ of the isosceles triangle $ABC$ ( $AB = BC$ ). The circle $\omega$ goes through $B$ and is tangent to $AC$ at $L$ . It intersects the line $AB$ at points $B$ and $D$ and the line $BC$ at points $B$ and $E$ . Let $M$ be the midpoint of the segment $DE$ and let $N\ne L$ be the intersection of the lines $BM$ and $AC$ . Given that $\frac{AN}{CN}=\frac{AL}{CL}> 1$ prove that the angle $A LB$ equals $60^o$ .

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