Problems(1)
Let ABC be a triangle with AB<AC. Let ω be a circle passing through B,C and assume that A is inside ω. Suppose X,Y lie on ω such that ∠BXA=∠AYC. Suppose also that X and C lie on opposite sides of the line AB and that Y and B lie on opposite sides of the line AC. Show that, as X,Y vary on ω, the line XY passes through a fixed point.Proposed by Aaron Thomas, UK