## What does it mean if a circle circumscribed a triangle?

circumcenter

When a circle circumscribes a triangle, the triangle is inside the circle and the triangle touches the circle with each vertex. The point where the perpendicular bisectors intersect is the center of the circle. The center point of the circumscribed circle is called the “circumcenter.”

## What is the radius of a circle that is circumscribed about a triangle?

For a triangle △ABC, let s = 12 (a+b+ c). Then the radius R of its circumscribed circle is R=abc4√s(s−a)(s−b)(s−c). In addition to a circumscribed circle, every triangle has an inscribed circle, i.e. a circle to which the sides of the triangle are tangent, as in Figure 12.

**What is the formula for circumscribed circle?**

An equation for the circumcircle in trilinear coordinates x : y : z is a/x + b/y + c/z = 0. An equation for the circumcircle in barycentric coordinates x : y : z is a2/x + b2/y + c2/z = 0.

### What circumscribed mean?

circumscribe \SER-kum-skrybe\ verb. 1 a : to constrict the range or activity of definitely and clearly. b : to define or mark off carefully. 2 a : to draw a line around. b : to surround by or as if by a boundary.

### What is the equation of the circle inscribed in a triangle?

Given A, B, and C as the sides of the triangle and A as the area, the formula for the radius of a circle circumscribing a triangle is r = ABC / 4A and for a circle inscribed in a triangle is r = A / S where S = (A + B + C) / 2.

**Why is the circumcircle important?**

A triangles’ circumcenter is very relevant. If you were navigating a boat, you could be lost at sea without its knowledge. In coastal navigation, a triangle’s circumcircle is sometimes used as a way of obtaining a position line using a sextant when no compass is available.

#### What is Circumradius and Inradius?

Inradius The inradius( r ) of a regular triangle( ABC ) is the radius of the incircle (having center as l), which is the largest circle that will fit inside the triangle. Circumradius: The circumradius( R ) of a triangle is the radius of the circumscribed circle (having center as O) of that triangle.

#### How do you find the area of an equilateral triangle circumscribed in a circle?

We know that area of circle = π*r2, where r is the radius of given circle. We also know that radius of Circumcircle of an equilateral triangle = (side of the equilateral triangle)/ √3. Therefore, area = π*r2 = π*a2/3.

**What is the meaning of Demark?**

archaic. to remove all trace of (a person or thing)

## How do you construct an equilateral triangle?

Construct a 60˚Angle by Constructing An Equilateral Triangle. Step 1 : Mark the point B on the line. Step 2 : Stretch the compasses to any width. Put the sharp end of the compasses at point B and draw an arc on the line. Label the point where the arc intersects the line as point C. Step 3: While keeping the sharp end…

## What is the formula for an equilateral triangle?

In a triangle, all interior angles total to 180 degrees. No two angles can total to 180 degrees or more; in an equilateral triangle, all angles are equal, or 180 degrees/3. The formula for the area is the square root (3)/4 * (s * s).

**Does equilateral triangle have three congruent sides?**

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry , an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle.

### Are two equilateral triangle always similar?

An equilateral triangle is a regular polygon with 3 sides, so all equilateral triangles are similar. We will use this in the following geometry problem.