ABC is an equilateral triangle. A1,B1,C1 are the midpoints of BC,CA,AB respectively. p is an arbitrary line through A1. q and r are lines parallel to p through B1 and C1 respectively. p meets the line B1C1 at A2. Similarly, q meets C1A1 at B2, and r meets A1B1 at C2. Show that the lines AA2,BB2,CC2 meet at some point X, and that X lies on the circumcircle of ABC. geometrycircumcirclegeometry proposed