Lumberjack physics

A perfectly symmetrical tree has a trunk in the shape of a cylinder with diameter 0.2 m. Since the tree is symmetrical the center of mass is at some distance L above the ground along the axis of the cylinder. A rotten lumberjack with no concept that he's cutting down the most amazing tree ever grown uses a chain saw to cut the tree down. He saws horizontally right at the base of the tree (ground level). What is the minimum value of L in meters such that the tree begins to topple over as soon once the chain saw reaches the position in the picture?

Details and assumptions

• The chain saw blade is 8 cm wide and 0.5 cm high.
• Treat the tree as a rigid body.