# Definition:Circle/Semicircle

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## Definition

In the words of Euclid:

*A***semicircle**is the figure contained by the diameter and the circumference cut off by it. And the center of the semicircle is the same as that of the circle.

(*The Elements*: Book $\text{I}$: Definition $18$)

In the above diagram, the region bounded by the straight line segment $CD$ and the arc $DBC$ is a **semicircle**.

Also, the region bounded by the straight line segment $CD$ and the arc $DFEC$ is a **semicircle**.

### Center of Semicircle

The **center** of a semicircle is defined as being the same as the center of the circle from which the semicircle is taken.

### Diameter

The **diameter** of a semicircle is the diameter of the circle from which the semicircle is derived.

## Also known as

A **semicircle** is also seen referred to as a **hemicycle**, but this is uncommon.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**hemicycle** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**semicircle**