• Corpus ID: 10473822

Solutions for 2010 Apmo Problems

  title={Solutions for 2010 Apmo Problems},
Problem 1. Let ABC be a triangle with ∠BAC = 90 •. Let O be the circumcenter of the triangle ABC and let Γ be the circumcircle of the triangle BOC. Suppose that Γ intersects the line segment AB at P different from B, and the line segment AC at Q different from C. Let ON be a diameter of the circle Γ. Prove that the quadrilateral AP N Q is a parallelogram. Solution: From the assumption that the circle Γ intersects both of the line segments AB and AC, it follows that the 4 points N, C, Q, O are…