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angle chasing given AB = ID and AH = OH , orthocenter, incenter, circumcenter

Source: 2013 Saudi Arabia GMO TST day III p3

July 31, 2020
geometryincenterCircumcenterorthocenterequal segmentscircumcircle

Problem Statement

ABCABC is a triangle, HH its orthocenter, II its incenter, OO its circumcenter and ω\omega its circumcircle. Line CICI intersects circle ω\omega at point DD different from CC. Assume that AB=IDAB = ID and AH=OHAH = OH. Find the angles of triangle ABCABC.
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