MathDB

5

Part of 2022 Thailand Online MO

Problems(1)

OXY and HBC are similar (complex moment)

Source: 2022 Thailand Online MO P5

4/4/2022
Let ABCABC be an acute triangle with circumcenter OO and orthocenter HH. Let MBM_B and MCM_C be the midpoints of ACAC and ABAB, respectively. Place points XX and YY on line BCBC such that ∠HMBX=∠HMCY=90∘\angle HM_BX = \angle HM_CY = 90^{\circ}. Prove that triangles OXYOXY and HBCHBC are similar.
geometrysimilar trianglesgeometry solvedThailandThailand online MOAngle Chasingreflection