Perimeter

Weekly Problem 44 - 2009
A garden has the shape of a right-angled triangle. A fence goes from the corner with the right-angle to a point on the opposite side. How long is the fence?

Tom and Jerry start with identical sheets of paper. Each one cuts his sheet in a different way. Can you find the perimeter of the original sheet?

Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.

Weekly Problem 8 - 2010
Are you able to find triangles such that these five statements are true?

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.