Παρασκευή, 13 Οκτωβρίου 2017

2004 JBMO Shortlist 7

Two circles $C_1$ and $C_2$ intersect in points $A$ and $B$. A circle $C$ with center in $A$ intersect $C_1$ in $M$ ​​and $P$ and $C_2$ in $N$ and $Q$ so that $N$ and $Q$ are located on different sides wrt $MP$, and $AB> AM$. Prove that  $\angle MBQ =  \angle NBP$.

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