Grade 9 2020 Problem 3

AnglesGeometryIncircleOrthocenterTriangle

U šiljastokutnom trokutu ABCABC vrijedi ∡BAC=60°\measuredangle BAC = 60° i ∣AB∣>∣AC∣|AB| > |AC|. Ako je II središte upisane kružnice, a HH ortocentar tog trokuta, dokaži da je 2∡AHI=3∡ABC2\measuredangle AHI = 3\measuredangle ABC.