几何部分1.本届IMO第4题.2.已知△ABC的外接圆T,边AB、AC的中点分别为M、N,圆T不含点A的弧BC的中点为T,△AMT、△ANT的外接圆与边AC、AB的中垂线分别交于点X、Y,且X、Y在△ABC的内部.若直线MN与XY交于点K,证明:KA=KT.3.在△ABC中,已知D、E分别为边CB、CA上的点,且AD、BE分别平分∠CAB彻、∠CBA.一个菱形内接于四边形AEDB(菱形的四个顶点分别 Geometry 1. The current IMO Question 4. 2 known △ ABC circumcircle T, the edge AB, AC midpoints are M, N, the circle T does not contain the point A of the arc BC of the midpoint of T, △ AMT, △ ANT circumcircle and the side of the AC, AB perpendicular perpendicular to the intersection of point X, Y, and X, Y in △ ABC if the line MN and XY intersect at point K, that: KA = KT .3. In ABC, D and E are known as points on CB and CA respectively, and AD and BE are respectively equal to ∠CAB and ∠CBA. A rhombus is inscribed in the quadrilateral AEDB (the four vertices of the rhombus