TANGENTIAL QUADRILATERAL Meaning and
Definition
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A tangential quadrilateral is a polygon that possesses an incircle, meaning that a circle can be inscribed within its four sides, touching each side at exactly one point. This type of quadrilateral is also commonly referred to as a cyclic quadrilateral or inscribed quadrilateral.
One characteristic of a tangential quadrilateral is that the sum of its opposite angles is always equal to 180 degrees. This property is known as the opposite angles property. Additionally, the opposite sides of a tangential quadrilateral are parallel and congruent. The diagonals of a tangential quadrilateral intersect each other at a right angle, and they are perpendicular bisectors of each other. These properties make the diagonals of a tangential quadrilateral particularly useful in finding various angles and side lengths within the figure.
The perimeter of a tangential quadrilateral can be determined by adding the lengths of all four sides together. Conversely, if the side lengths of the quadrilateral are known, the area can be calculated using formulas such as Brahmagupta's formula or Heron's formula.
Tangential quadrilaterals are encountered in various mathematical contexts, from geometry and trigonometry to advanced topics like circles and theorems related to quadrilaterals. They often serve as building blocks for more complex shapes and figures, and their properties can be applied to solve problems and establish relationships between angles, sides, and diagonals.
Etymology of TANGENTIAL QUADRILATERAL
The word "tangential" comes from the Latin word "tangens", which means "touching" or "to touch". In geometry, tangential refers to something that touches or is tangent to another object.
The term "quadrilateral" comes from the Latin words "quadri" meaning "four", and "latus" meaning "side". It refers to a polygon with four sides.
Therefore, the etymology of the term "tangential quadrilateral" is a combination of "tangential", meaning touching or tangent, and "quadrilateral", meaning a four-sided polygon. It describes a quadrilateral in which all sides are tangent to a circle or to a pair of non-intersecting circles.
