In the above diagram, each of the grid squares is a unit long. Also, all the arcs are quadrants. If the area of the shape enclosed by arcs , , , and can be represented as where are integers with positive, find the maximum value of .
Let be a square and be a point inside the square such that and . Find the area of
Find the area of region (four square looking region of central circle) if radius of each circle is 4 units.
As shown, a rectangle (not a square) is partitioned into four triangles: 1 equilateral and 3 right triangles. The areas of two of the right triangles are 30 and 50. Find the area of the remaining right triangle.
Bonus: Find the general relationship among the areas of the 3 right triangles.
Suppose we combine a unit circle and a square of the same area, as shown above, such that their centroids lie on the same point. What is the area of the non-overlapping white region?
If your answer is of the following form where and are positive integers, evaluate .