Let ABC be an acute triangle with orthocenter H and circumcircle Ω. Let M be the midpoint of side BC. Point D is chosen from the minor arc BC on Γ such that ∠BAD=∠MAC. Let E be a point on Γ such that DE is perpendicular to AM, and F be a point on line BC such that DF is perpendicular to BC. Lines HF and AM intersect at point N, and point R is the reflection point of H with respect to N. Prove that ∠AER+∠DFR=180∘. Proposed by Li4. geometrycircumcirclegeometric transformationreflection