Let ABC a triangle inscribed in a circle (O) with orthocenter H. Two lines d1 and d2 are mutually perpendicular at H. Let d1 meet BC,CA,AB at X1,Y1,Z1 respectively. Let A1B1C1 be a triangle formed by the line through X1 perpendicular to BC, the line through Y1 perpendicular to CA, the line through Z1 perpendicular perpendicular to AB. Triangle A2B2C2 is defined in the same manner. Prove that the circumcircles of triangles A1B1C1 and A2B2C2 touch each other at a point on (O).Nguyễn Văn Linh concurrent circlescirclestangent circlesorthocenter