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P3

Part of 2017 Sharygin Geometry Olympiad

Problems(1)

Orthocenter and tangency point are collinear

Source: Sharygin Geometry Olympiad Correspondence Round 2017 P-3 (Grade-8)

5/1/2017
Let II be the incenter of triangle ABCABC; HB,HCH_B, H_C the orthocenters of triangles ACIACI and ABIABI respectively; KK the touching point of the incircle with the side BCBC. Prove that HB,HCH_B, H_C and K are collinear. Proposed by M.Plotnikov
geometry