EXCIRCLE Meaning and
Definition
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An excircle refers to a geometric construct associated with a polygon, particularly a triangle. It is specifically an externally tangent circle to one side of the polygon, while also tangentially touching the extensions of the other two sides. The excircle lies outside the triangle, in contrast to the incircle, which is inscribed within it.
In more technical terms, an excircle is a circle that satisfies the following conditions: it is tangent to one of the sides of the triangle at a single point, and it is also tangent to the extensions of the remaining two sides. Thus, the excircle can be thought of as the largest circle that can be drawn outside the triangle using one of its sides as a tangent. Each of the three sides of a triangle has its corresponding excircle.
The excircle holds significance in various mathematical contexts, particularly in geometric constructions and calculations. It is commonly utilized to determine various properties of the triangle, such as the lengths of its sides, the angles formed by these sides, and the triangle's area. Additionally, the excircle helps in understanding and solving triangle-related problems, whether in pure mathematics or practical applications like engineering or architecture.
Common Misspellings for EXCIRCLE
- excipule
- wxcircle
- sxcircle
- dxcircle
- rxcircle
- 4xcircle
- 3xcircle
- ezcircle
- eccircle
- edcircle
- escircle
- exxircle
- exvircle
- exfircle
- exdircle
- excurcle
- excjrcle
- exckrcle
- excorcle
- exc9rcle
- exc8rcle
- exscicle
Etymology of EXCIRCLE
The word "excircle" is derived from the combination of two separate terms: "ex" and "circle".
The prefix "ex-" comes from the Latin word "ex", which means "out of" or "outside". This prefix is commonly used in English to indicate something that is external or excluding. For example, "export" means to send goods out of the country, "exclude" means to keep someone or something out, and "exit" refers to the way out of a place.
The word "circle" comes from the Latin noun "circulus", meaning "small ring" or "circular figure". This term was widely adopted in English to describe a two-dimensional geometric shape consisting of all points that are equidistant from a central point.
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