Circle properties and circle theorems

What is the same and what is different about these circle questions? What connections can you make?

How much of the field can the animals graze?

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?

Can you find a relationship between the area of the crescents and the area of the triangle?

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?