2009 OIM Problems/Problem 3

Problem

Let $C_1$ and $C_2$ be two circles with centers $O_1$ and $O_2$ with the same radius, which intersect at $A$ and $B$. Let $P$ be a point on the arc $AB$ of $C_2$ that is inside $C_1$. Line $AP$ intersects $C_1$ at $C$, line $CB$ intersects $C_2$ at $D$ and the bisector of $\angle CAD$ intersects $C_1$ at $E$ and $C_2$ at $L$. Let $F$ be the point symmetrical to $D$ with respect to the midpoint of $PE$. Show that there exists a point $X$ satisfying $\angle XFL = \angle XCD = 30^{\circ}$ and $CX = O_1O_2$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions