## Arc (geometry) |

In **arc** (symbol: **⌒**) is a **circular arc**. In space, if the arc is part of a **great arc**.

Every pair of distinct points on a circle determines two arcs. If the two points are not directly opposite each other, one of these arcs, the **minor arc**, will **major arc**, will subtend an angle greater than π radians.

- circular arcs
- parabolic arcs
- see also
- references
- external links

The length (more precisely, *L*, of an arc of a circle with radius *r* and subtending an angle *θ* (measured in radians) with the circle center — i.e., the ** central angle** — equals

Substituting in the circumference

and, with *α* being the same angle measured in degrees, since *θ* = *α*/180π, the arc length equals

A practical way to determine the length of an arc in a circle is to plot two lines from the arc's endpoints to the center of the circle, measure the angle where the two lines meet the center, then solve for L by cross-multiplying the statement:

- measure of
angle in degrees/360° =*L*/circumference.

For example, if the measure of the angle is 60 degrees and the circumference is 24 inches, then

This is so because the circumference of a circle and the degrees of a circle, of which there are always 360, are directly proportional.

The area of the sector formed by an arc and the center of a circle (bounded by the arc and the two radii drawn to its endpoints) is

The area *A* has the same proportion to the *θ* to a full circle:

We can cancel π on both sides:

By multiplying both sides by *r*^{2}, we get the final result:

Using the conversion described above, we find that the area of the sector for a central angle measured in degrees is

The area of the shape bounded by the arc and the straight line between its two end points is

To get the area of the

Using the *r* of a circle given the height *H* and the width *W* of an arc:

Consider the *W*, and it is divided by the bisector into two equal halves, each with length *W*/2. The total length of the diameter is 2*r*, and it is divided into two parts by the first chord. The length of one part is the *H*, and the other part is the remainder of the diameter, with length 2*r* − *H*. Applying the intersecting chords theorem to these two chords produces

whence

so

Other Languages

العربية: قوس (هندسة)

asturianu: Arcu (xeometría)

беларуская: Дуга (геаметрыя)

brezhoneg: Gwareg (geometriezh)

català: Arc (geometria)

dolnoserbski: Pšužyna

eesti: Kaar

emiliàn e rumagnòl: Êrc (giumetrìa)

español: Arco (geometría)

Esperanto: Arko (geometrio)

euskara: Arku (geometria)

فارسی: کمان (هندسه)

français: Arc (géométrie)

Gaeilge: Stua

galego: Arco (xeometría)

한국어: 호 (기하학)

hrvatski: Luk (matematika)

italiano: Arco (geometria)

latviešu: Loks (matemātika)

मराठी: कंस (चाप)

Nederlands: Boog (meetkunde)

日本語: 弧 (幾何学)

norsk: Bue (geometri)

norsk nynorsk: Boge

ਪੰਜਾਬੀ: ਚਾਪ

ភាសាខ្មែរ: ធ្នូរង្វង់

polski: Łuk krzywej

português: Arco (matemática)

srpskohrvatski / српскохрватски: Luk (matematika)

suomi: Ympyrän kaari

தமிழ்: வில் (வடிவவியல்)

татарча/tatarça: Дуга

తెలుగు: చాపం

Türkçe: Yay (geometri)

Tiếng Việt: Cung (hình học)

吴语: 弧

中文: 弧