: The proof relies on showing that two specific triangles involving these points are similar. By establishing similarity, the equality of subtended angles at the circle's circumference confirms the points lie on a common circle. Problem 4 (Integer Sequences) : For a sequence , find all is a perfect -th power for : Analysis starts by proving that
In circle 1, angle between tangent at C and chord CA equals angle in opposite segment CBA. Similarly, in circle 2, angle between tangent at D and chord DA equals angle DBA. bmo 2008 solutions
Assume for contradiction that every pair of adjacent squares differs by at most 8. Then moving from any square to an adjacent square changes the value by at most 8. But how does that restrict the arrangement? : The proof relies on showing that two
BMO1 2008/2009 Solutions - The British Mathematical Olympiad Similarly, in circle 2, angle between tangent at