# circumcircle

## 09 Dimensions of smaller equilateral triangle inside the circle

**Problem**

From the figure shown, ABC and DEF are equilateral triangles. Point E is the midpoint of AC and points D and F are on the circle circumscribing ABC. If AB is 12 cm, find DE.

- Read more about 09 Dimensions of smaller equilateral triangle inside the circle
- Log in or register to post comments
- 2947 reads

## Derivation of Formula for Radius of Circumcircle

The formula for the radius of the circle circumscribed about a triangle (circumcircle) is given by

where A_{t} is the area of the inscribed triangle.

- Read more about Derivation of Formula for Radius of Circumcircle
- Log in or register to post comments
- 52109 reads

## Centers of a Triangle

This page will define the following: incenter, circumcenter, orthocenter, centroid, and Euler line.

**Incenter**

Incenter is the center of the inscribed circle (incircle) of the triangle, it is the point of intersection of the angle bisectors of the triangle.

The radius of incircle is given by the formula

where A_{t} = area of the triangle and s = ½ (a + b + c). See the derivation of formula for radius of incircle.

- Read more about Centers of a Triangle
- Log in or register to post comments
- 13351 reads