# Sector of a Circle

## Smallest Part From The Circle That Was Divided Into Four Parts By Perpendicular Chords

**Problem**

Divide the circle of radius 13 cm into four parts by two perpendicular chords, both 5 cm from the center. What is the area of the smallest part.

## 06 Circular arcs inside and tangent to an equilateral triangle

**Example 06**

The figure shown below is an equilateral triangle of sides 20 cm. Three arcs are drawn inside the triangle. Each arc has center at one vertex and tangent to the opposite side. Find the area of region enclosed by these arcs. The required area is shaded as shown in the figure below.

## 05 Three identical cirular arcs inside a circle

## 04 Four overlapping semi-circles inside a square

**Example 04**

The figure shown below consists of arcs of four semi-circles with centers at the midpoints of the sides of a square. The square measures 20 cm by 20 cm. Find the area bounded by these circular arcs shaded in the figure shown.

## 03 Area enclosed by pairs of overlapping quarter circles

**Example 03**

The shaded regions in the figure below are areas bounded by two circular arcs. The arcs have center at the corners of the square and radii equal to the length of the sides. Calculate the area of the shaded region.

## 02 Area bounded by arcs of quarter circles

**Example 02**

Arcs of quarter circles are drawn inside the square. The center of each circle is at each corner of the square. If the radius of each arc is equal to 20 cm and the sides of the square are also 20 cm. Find the area common to the four circular quadrants. See figure below.

## 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.

## 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.