Subcontests
(6)Circle in triangle
A circle ω is strictly inside triangle ABC. The tangents from A to ω intersect BC in A1,A2 define B1,B2,C1,C2 similarly. Prove that if five of six points A1,A2,B1,B2,C1,C2 lie on a circle the sixth one lie on the circle too. a number theory problem that makes you want to count
For all prime p>3 with reminder 1 or 3 modulo 8 prove that the number triples (a,b,c),p=a2+bc,0<b<c<p is odd.Proposed by Navid Safaie Trapezoid And Segment
In a trapezoid ABCD with AD parallel to BC points E,F are on sides AB,CD respectively. A1,C1 are on AD,BC such that A1,E,F,A lie on a circle and so do C1,E,F,C. Prove that lines A1C1,BD,EF are concurrent.