EE-MO 2001

John had to solve a math problem in the class. While cleaning the blackboard, he accidentally erased a part of his problem as well: the text that remained on board was $37 \cdot(72 + 3x) = 14**45$ , where $*$ marks an erased digit. Show that John can still solve his problem, knowing that $x$ is an integer

A circle of radius $10$ is tangent to two adjacent sides of a square and intersects its two remaining sides at the endpoints of a diameter of the circle. Find the side length of the square.