An ellipse that has its center at the origin, its semi-major axis along the x-axis, and passes through the point (6, 4) shares the same orthoptic circle as a hyperbola that has its semi-major axis along the x-axis and passes through the point (17, 16/3). If both semi-major axes are integers and have a 2/3 ratio, then the area of the orthoptic circle is kπ. Find k.
A circle has a radius of 12 units and its center is at one vertex of a square. The square has a side of 12 units. Find the area of the shaded region?
A square is in the first quadrant, as shown, with its sides extending to points on the x-axis of (3, 0), (5, 0), (7, 0) and (13, 0). What is the area of the square?
Let ABC be an equilateral triangle. Let P be any point on its incircle. Prove that:
AP2 + BP2 + CP2 = k for some constant k
Square ABCD has a side length of 4. Construct a quarter circle with radius 4 centered at B and a semi-circle with diameter AD. What is the area of overlap between the quarter circle and semicircle?
