# Thread: Points on circles collinear

1. ## Points on circles collinear

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Diagonals of quadrilateral $ABCD$ intersect in point $S$. Circle $k_1$ is circumscribed of triangle $ABS$. $k_1$ intersects line $BC$ in point $M$. Circle $k_2$ is circumscribed of triangle $ADS$ and it intersects line $CD$ in point $N$. Prove that points $S, M$ and $N$ are collinear.

2. ## Re: Points on circles collinear

Originally Posted by kicma
Last one...

Diagonals of quadrilateral $ABCD$ intersect in point $S$. Circle $k_1$ is circumscribed of triangle $ABS$. $k_1$ intersects line $BC$ in point $M$. Circle $k_2$ is circumscribed of triangle $ADS$ and it intersects line $CD$ in point $N$. Prove that points $S, M$ and $N$ are collinear.

are you sure about the wording of the question? S, M, and N don't look colinear to me. The picture isn't perfect but it's pretty accurate.

Looking at it the only two points, one on CD and one on BC that are going to be colinear with S are B and D.

3. ## Re: Points on circles collinear

I forgot to say that ABCD is tangential quadrilateral.