escribed

A circle is escribed to a triangle, touching one side and the extensions of the other two.

Definition

1. Adjective (Mathematics):
   • Externally tangent: In geometry, "escribed" describes a circle that is tangent to one side of a triangle and the extensions of the other two sides. Such a circle is called an escribed circle or excircle.

Usage Examples

• (A circle externally tangent to one side and two extended sides of a triangle.)
• (Describing the excircles of a triangle.)

Advanced Usage

• "escribed circle": also known as an excircle; it is the circle tangent to one side of a triangle and the extensions of the other two sides.

  • The radius of the escribed circle opposite vertex A is denoted as r_a. (The excircle's radius associated with side a.)

• "escribed triangle": a triangle formed by the centers of the three escribed circles of a given triangle.

  • The escribed triangle is also called the excentral triangle. (The triangle connecting the excenters.)

Variants and Related Words

• Escribe (verb): to draw or describe a circle tangent to one side of a triangle and the extensions of the other two sides.

  • To escribe a circle to a triangle, one must construct it externally. (To draw an excircle.)

• Excircle (noun): a synonym for "escribed circle".

  • Each triangle has three excircles. (Three escribed circles.)

Synonyms

• Excircle: a circle tangent to one side of a triangle and the extensions of the other two sides.
• External tangent circle: a circle tangent to a triangle externally.

Related Idioms