09 Dimensions of smaller equilateral triangle inside the circle

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.

Two equilateral triangles inside a circle


Derivation of Formula for Radius of Circumcircle

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

$R = \dfrac{abc}{4A_t}$

where At is the area of the inscribed triangle.

Centers of a Triangle

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

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

$r = \dfrac{A_t}{s}$

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

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