# Either of two unit circles passes through the center of the other. How do you prove that the common area is #2/3pi-sqrt 3/2# areal units?

##### 2 Answers

Proved in the explanation

#### Explanation:

The common area is enclosed by unit circle arcs subtending

For this arc, sector area of a unit circle

One half of the common area

= this sector area less area of the inner triangle, of sides

Twice this is the common area =

I welcome a graphical depiction,.from an interested reader.

see explanation.

#### Explanation:

1) Equilateral triangle area

2) yellow area

3) Common area