Question 143
Let $ABC$ be an isosceles triangle in $A$. Let $M$ and $N$ two points of $[BC]$. The straight lines $[AM]$ and $[AN]$ intersect the circle circumscribed with $ABC$ in $P$ and $Q$. 1) Show that $M, N, P, Q$ are cocyclic. 2) Let $R_{1}$ and $R_{2}$ be the radii of the circles circumscribed to $BMP$ and $CMP$. Calculate $R_{1}+R_{2}$ based on lengths $AB$ and $BC$.