Race to the Tree!

Johnny and you were playing a game. Johnny was standing $10$m away from the centre of a circular tree with a radius of $1$m, while you were standing on the opposite side of the tree, also $10$m away from the centre, so that the tree blocked his view of you. The game was that if you could reach the tree (its edge, $1$m from the centre) without being seen, you would win, but if Johnny could see you without his line of sight being blocked by the tree, he would win.
When the game starts, you run in a straight line towards the centre of the tree at a constant speed, while Johnny may run in any direction at $5$m/s. Treat both of you as points. What was the minimum constant speed you had to run at to win the game?