IMO 2024 Shortlist G2
Let ABC be a triangle with AB ă AC ă BC, incentre I and incircle ω. Let X be the point in the interior of side BC such t...
Category: Geometry
Problem
Let ABC be a triangle with AB ă AC ă BC, incentre I and incircle ω. Let X be the point in the interior of side BC such that the line through X parallel to AC is tangent to ω. Similarly, let Y be the point in the interior of side BC such that the line through Y parallel to AB is tangent to ω. Let AI intersect the circumcircle of triangle ABC again at P ‰ A. Let K and L be the midpoints of AB and AC, respectively. Prove that =KIL ` =Y PX “ 180˝ . (Poland)