## What is the formula of distance between incenter and circumcenter?

Hence it is proved that the distance between the circumcenter and the incenter of the triangle ABC is $\sqrt {{R^2} – 2Rr} $.

## What is the relation between incircle and circumcircle?

The circumcircle of a triangle is the unique circle determined by the three vertices of the triangle. Its center is called the circumcenter (blue point) and is the point where the (blue) perpendicular bisectors of the sides of the triangle intersect. The incircle of a triangle is the circle inscribed in the triangle.

**What is the formula of circumcentre?**

Let O (x, y) be the circumcenter of ∆ ABC. Then, the distances to O from the vertices are all equal, we have AO = BO = CO = Circumradius. By solving these two linear equations using a substitution or elimination method, the coordinates of the circumcenter O (x, y) can be obtained.

**What is the distance between Orthocentre and Circumcentre?**

Triangle ABC is right-angled at the point A. Therefore, orthocenter lies on the point A which is (0, 0). The co-ordinate of circumcenter is (2.5, 6). Therefore, the distance between the orthocenter and the circumcenter is 6.5.

### What is the ratio of radius of incircle to circumcircle?

In an equilateral triangle, the ratio of the radius of circumcircle to that of incircle Is 2:1. In an equilateral triangle, altitude, perpendicular bisectors, angle bisectors, and medians are the same. In an equilateral triangle, centroid, circumcentre, incentre, and ortho center are the same.

### What is the formula for radius of incircle?

Calculating the radius 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 incentre and circumcentre?**

The incentre of a circle is also the centre of the circle which touches all the sides of the triangle. Circumcentre and Circumcircle: The point of intersection of the perpendicular bisectors of the sides of a triangle ABC is called its circumcentre.