Let ABC be an acute scalene triangle, and let A1,B1,C1 be the feet of the altitudes from A,B,C. Let A2 be the intersection of the tangents to the circle ABC at B,C and define B2,C2 similarly. Let A2A1 intersect the circle A2B2C2 again at A3 and define B3,C3 similarly. Show that the circles AA1A3,BB1B3, and CC1C3 all have two common points, X1 and X2 which both lie on the Euler line of the triangle ABC.United Kingdom, Joe Benton geometryEuler LineRMMRMM 2020RMM Shortlist