Trigonometry · Superchallenge problem

A square panel with side $10$ stands upright in a vertical plane that is perpendicular to a wall. One corner of the panel rests on the floor, the next corner touches the wall, and the rest of the panel is above the floor and away from the wall. The highest corner of the panel is $14$ above the floor. Find the distance from the centre of the panel to the line where the wall meets the floor.