# Semicircle

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In mathematics (more specifically geometry), a **semicircle** is a two-dimensional geometric shape that forms half of a circle. Being half of a circle's 360°, the arc of a semicircle always measures 180°. A triangle inscribed in a semicircle is always a right triangle.

## Uses

A semicircle can be used to construct arithmetic and geometric means of two lengths using straight-edge and compass. If we make a semicircle with a diameter of *a*+*b*, then the length its radius is the arithmetic mean (since it's half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths *a* and *b*, and then connecting their common end and the semicircle with a segment perpendicular to the diameter. The length of the resulting segment is the geometric mean^{[1]}, which can be proved using Pythagorean theorem.

This method can be used to accomplish quadrature of a rectangle (since a square whose sides are equal to geometric mean of sides of a rectangle has the same area as the rectangle), and thus any figure for which we can construct a rectangle with equal area, such as any polygon (but not a circle).

### Area and Perimeter

The area is:

The perimeter is:

## Circumscribed Semicircle

The area is:

The perimeter is:

## Inscribed Semicircle

The area is:

The perimeter is: