From the figure shown below, O1, O2, and O3 are centers of circles located at the midpoints of the sides of the triangle ABC. The sides of ABC are diameters of the respective circles. Prove that
$A_1 + A_2 + A_3 = A_4$
where A1, A2, A3, and A4 are areas in shaded regions.
Conic sections can be defined as the locus of point that moves so that the ratio of its distance from a fixed point called the to its distance from a fixed line called the is constant. The constant ratio is called the eccentricity of the conic.
The figure shown below are circular arcs with center at each corner of the square and radius equal to the side of the square. It is desired to find the area enclosed by these arcs. Determine the area of the shaded region.