1. ## Proof

Given triangle MNL.Line XY is ll to base NL.The line XY intersects the triangle at points X and Y.X lies on MN and Y on ML.The circle passes through X and is tangent to ML at Y,it is intersects triangle at point S(that point lies between X and N).How to prove that the points S,Y,L,N lie on the circle.

I know that we need to prove that quad SYLN is cyclic,but how??

2. Originally Posted by RE1
Given triangle MNL.Line XY is ll to base NL.The line XY intersects the triangle at points X and Y.X lies on MN and Y on ML.The circle passes through X and is tangent to ML at Y, it intersects triangle at point S (that point lies between X and N).How to prove that the points S,Y,L,N lie on the circle.

I know that we need to prove that quad SYLN is cyclic,but how??
[The N that I highlighted in red should be M.]

A quadrilateral is cyclic if opposite angles add up to 180º. Show that the angles LNM and MYS are equal. It will follow that the angles LNS and SYL have sum 180º, and so the quadrilateral SYLN is cyclic.

3. Can you give me some hint how to do so.I know that triangles MXY and NML are similar.
Also I was thinking about Ptolemy's theorem.I still cannot find the way to show that these angles are equal.