# What do you mean by circumcircle?

## What do you mean by circumcircle?

Definition of circumcircle : a circle which passes through all the vertices of a polygon (such as a triangle)

Table of Contents

### What is Exradius of a triangle?

The circle with centre I₁ and touching the three sides of the triangle is called excircle of triangle ABC opposite to the vertex A. The radius of this ex-circle is called ex-radius of triangle ABC and it is denoted by r₁. The excentres of ΔABC opposite to the vertices B, C are respectively denoted by I₂, I₃.

**What is the formula of circumcircle?**

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

**What is circumcircle Class 9?**

The circle which passes through all the vertices of any given geometrical figure or a polygon, without crossing the figure. This is also termed as circumcircle.

## What is the formula of Exradius?

The exradii of a triangle with sides a, b, c are given by ra = ∆ s – a , rb = ∆ s – b , rc = ∆ s – c . (a + b + c). r ra =s – a s .

### What is Incentre and Excentre?

A point where the bisector of one interior angle and bisectors of two external angle bisectors of the opposite side of the triangle, intersect is called the excenter of the triangle. There are in all three excentres of a triangle.

**How is incircle formed?**

The incenter of a triangle is the point of intersection of the perpendicular bisectors of the triangle. The incenter of a triangle is the point of intersection of the perpendicular bisectors of the triangle.

**What is Circumcentre and Orthocentre?**

circumcenter O, the point of which is equidistant from all the vertices of the triangle; incenter I, the point of which is equidistant from the sides of the triangle; orthocenter H, the point at which all the altitudes of the triangle intersect; centroid G, the point of intersection of the medians of the triangle.

## What is Escribed radius?

The circle which touches the sidesBC and two sides AB and AC produced of a triangle ABC is called the Escribed circle opposite to the angle A. Its radius is denoted by r1.

### How do you make a excircle?

In order to construct the excircles, we must first extend all the sides of the triangles. Next, we have to bisect the exterior angles that are between the two extended sides to which the triangle will be tangent. The intersection of the angle bisectors is the center of that excircle.

**What is Incentre formula?**

Incenter of a Triangle Properties If I is the incenter of the triangle ABC, then ∠BAI = ∠CAI, ∠BCI = ∠ACI and ∠ABI = ∠CBI (using angle bisector theorem). The sides of the triangle are tangents to the circle, and thus, EI = FI = GI = r known as the inradii of the circle or radius of incircle.

**What is Excentre of triangle?**

Excentre of a triangle is the point of concurrency of bisectors of two exterior and third interior angle. Hence there are three excentres I1, I2 and I3 opposite to three vertices of a triangle.

## What is circumcircle radius?

The circumradius of a cyclic polygon is the radius of the circumscribed circle of that polygon. For a triangle, it is the measure of the radius of the circle that circumscribes the triangle. Since every triangle is cyclic, every triangle has a circumscribed circle, or a circumcircle.

### What is the radius of incircle?

Its radius, the inradius (usually denoted by r) is given by r = K/s, where K is the area of the triangle and s is the semiperimeter (a+b+c)/2 (a, b and c being the sides).

**What is incenter point?**

Simply construct the angle bisectors of the three angles of the triangle. The point where the angle bisectors intersect is the incenter. Actually, finding the intersection of only 2 angle bisectors will find the incenter.