This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2016 Balkan MO, 2
Let $ABCD$ be a cyclic quadrilateral with $AB<CD$. The diagonals intersect at the point $F$ and lines $AD$ and $BC$ intersect at the point $E$. Let $K$ and $L$ be the orthogonal projections of $F$ onto lines $AD$ and $BC$ respectively, and let $M$, $S$ and $T$ be the midpoints of $EF$, $CF$ and $DF$ respectively. Prove that the second intersection point of the circumcircles of triangles $MKT$ and $MLS$ lies on the segment $CD$. [i](Greece - Silouanos Brazitikos)[/i]
cyclic quadrilateral bir tiyinga qimmat masala geometry euler circle Menelaus' theorem angle chasing congruent triangles cyclic quadrilaterals homothety law of sines

2016 Balkan MO Shortlist, G2
Let $ABCD$ be a cyclic quadrilateral with $AB<CD$. The diagonals intersect at the point $F$ and lines $AD$ and $BC$ intersect at the point $E$. Let $K$ and $L$ be the orthogonal projections of $F$ onto lines $AD$ and $BC$ respectively, and let $M$, $S$ and $T$ be the midpoints of $EF$, $CF$ and $DF$ respectively. Prove that the second intersection point of the circumcircles of triangles $MKT$ and $MLS$ lies on the segment $CD$. [i](Greece - Silouanos Brazitikos)[/i]
cyclic quadrilateral bir tiyinga qimmat masala geometry euler circle Menelaus' theorem angle chasing congruent triangles cyclic quadrilaterals homothety law of sines