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.
 

011-three-tangent-circles.gif

 

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 m2
B. 63.7 m2
C. 128.7 m2
D. 99.5 m2
 

Part 2: What is the total water surface area?
A. 409.4 m2
B. 524.3 m2
C. 387.3 m2
D. 427.5 m2
 

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
 

05 Three identical cirular arcs inside a circle Jhun Vert Fri, 05/01/2020 - 09:33 pm

Example 05
Circular arcs of radii 10 cm are described inside a circle of radius 10 cm. The centers of each arc are on the circle and so arranged so that they are equally distant from each other. Find the area enclosed by three arcs shown as shaded regions in the figure.
 

Overlapping arcs inside a circle

 

The Circle

Video

The following are short descriptions of the circle shown below.

Tangent
Tangent is a line that would pass through one point on the circle.
Secant
Secant is a line that would pass through two points on the circle.
Chord
Chord is a secant that would terminate on the circle itself.
Diameter, d
Diameter is a chord that passes through the center of the circle.
Radius, r
Radius is one-half of the diameter.

 

The Circle