# segment of a circle

## 11 - Area inside a circle but outside three other externally tangent circles

**Problem 11**

Three identical circles of radius 30 cm are tangent to each other externally. A fourth circle of the same radius was drawn so that its center is coincidence with the center of the space bounded by the three tangent circles. Find the area of the region inside the fourth circle but outside the first three circles. It is the shaded region shown in the figure below.

## 10 Swimming pool in the shape of two intersecting circles

**Situation**

A swimming pool is shaped from two intersecting circles 9 m in radius with their centers 9 m apart.

Part 1: What is the area common to the two circles?

A. 85.2 m^{2}

B. 63.7 m^{2}

C. 128.7 m^{2}

D. 99.5 m^{2}

Part 2: What is the total water surface area?

A. 409.4 m^{2}

B. 524.3 m^{2}

C. 387.3 m^{2}

D. 427.5 m^{2}

Part 3: What is the perimeter of the pool, in meters?

A. 63.5 m

B. 75.4 m

C. 82.4 m

D. 96.3 m

## 09 Areas outside the overlapping circles indicated as shaded regions

**Problem**

From the figure shown, AB = diameter of circle O_{1} = 30 cm, BC = diameter of circle O_{2} = 40 cm, and AC = diameter of circle O_{3} = 50 cm. Find the shaded areas A_{1}, A_{2}, A_{3}, and A_{4} and check that A_{1} + A_{2} + A_{3} = A_{4} as stated in the previous problem.

## 07 Area inside the larger circle but outside the smaller circle

**Problem**

From the figure shown below, DE is the diameter of circle A and BC is the radius of circle B. If DE = 60 cm and AC = 10 cm, find the area of the shaded region.

## 05 Three identical cirular arcs inside a circle

## 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.

## 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.

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