MathDB

XI.15

Part of Ukrainian TYM Qualifying - geometry

Problems(1)

IW_1+ IW_2 + IW_3>= 2R + \sqrt{2Rr} , incenter, circumcircle

Source: XI All-Ukrainian Tournament of Young Mathematicians, Qualifying p15

5/27/2021
Let II be the point of intersection of the angle bisectors of the △ABC\vartriangle ABC, W1,W2,W3W_1,W_2,W_3 be point of intersection of lines AI,BI,CIAI, BI, CI with the circle circumscribed around the triangle, rr and RR be the radii of inscribed and circumscribed circles respectively. Prove the inequality IW1+IW2+IW3≥2R+2Rr.IW_1+ IW_2 + IW_3\ge 2R + \sqrt{2Rr.}
geometryincenterinequalitiescircumcircleUkrainian TYM