Subcontests
(4)Taiwanese Geometry
Given a triangle △ABC. Denote its incircle and circumcircle by ω,Ω, respectively. Assume that ω tangents the sides AB,AC at F,E, respectively. Then, let the intersections of line EF and Ω to be P,Q. Let M to be the mid-point of BC. Take a point R on the circumcircle of △MPQ, say Γ, such that MR⊥EF. Prove that the line AR, ω and Γ intersect at one point. Almost Symmetric Inequality
Prove that for any positive reals a,b,c,d with a+b+c+d=4, we have cyc∑a2+ab+b23a3+cyc∑a+b2ab≥8