Πέμπτη, 12 Οκτωβρίου 2017

2005 JBMO problem 2

Let ${ABC}$  be an acute-angled triangle inscribed in a circle ${k}$. It is given that the tangent from ${A}$  to the circle meets the line ${BC}$  at point ${P}$. Let ${M}$  be the midpoint of the line segment ${AP}$  and ${R}$  be the second intersection point of the circle ${k}$  with the line ${BM}$. The line ${PR}$  meets again the circle ${k}$  at point ${S}$  different from ${R}$. Prove that the lines ${AP}$  and ${CS}$  are parallel.

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