Circle

Problem
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
 

where A₁, A₂, A₃, and A₄ are areas in shaded regions.
 

Definition
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 focus to its distance from a fixed line called the directrix is constant. The constant ratio is called the eccentricity of the conic.
 

Example
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.
 

Problem 01
Find the shape of the rectangle of maximum perimeter inscribed in a circle.
 

Example 3
Find the area inside the cardioid r = a(1 + cos θ) but outside the circle r = a.
 

The following are short descriptions of the circle shown below.