# Circle

## 08 Circles with diameters equal to corresponding sides of the triangle

**Problem**

From the figure shown below, O_{1}, O_{2}, and O_{3} 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 A_{1}, A_{2}, A_{3}, and A_{4} are areas in shaded regions.

## Conic Sections

**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.

- Read more about Conic Sections
- Add new comment
- 43402 reads

## 01 Arcs of quarter circles

**Example 01**

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.

## 01 Rectangle of maximum perimeter inscribed in a circle

**Problem 01**

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

## 03 Area Inside the Cardioid r = a(1 + cos θ) but Outside the Circle r = a

**Example 3**

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

## The Circle

The following are short descriptions of the circle shown below.

Secant - is a line that would pass through two points on the circle.

Chord - is a secant that would terminate on the circle itself.

Diameter, d - is a chord that passes through the center of the circle.

Radius, r - is one-half of the diameter.

- Read more about The Circle
- Add new comment
- 21194 reads