Problem

Source: Moscow mathematic olympiad 2022, Day 2 P11.4

Tags: geometry, trapezoid



A diagonal is drawn in an isosceles trapezoid. By the contour of each of the resulting two triangles creeps its own beetle. The velocities of the beetles are constant and identical. Beetles don't change directions around their contours, and along the diagonal of the trapezoid they crawl in different directions. Prove that for any starting positions of the beetles they will ever meet.