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8.3

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 8.3 concyclic

Source:

6/7/2020
Let ABCABC be a scalene triangle, (O)(O) and HH be the circumcircle and its orthocenter. A line through AA is parallel to OHOH meets (O)(O) at KK. A line through KK is parallel to AHAH, intersecting (O)(O) again at LL. A line through LL parallel to OAOA meets OHOH at EE. Prove that B,C,O,EB,C,O,E are on the same circle.
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Concycliccircumcircleorthocentergeometry