Problem

Source: Iranian National Olympiad (3rd Round) 2003

Tags: vector, trigonometry, geometry, trapezoid, absolute value, trig identities, Law of Cosines



Circles $ C_1,C_2$ intersect at $ P$. A line $ \Delta$ is drawn arbitrarily from $ P$ and intersects with $ C_1,C_2$ at $ B,C$. What is locus of $ A$ such that the median of $ AM$ of triangle $ ABC$ has fixed length $ k$.