Question

Triangle ABC is an equilateral triangle. The angle bisectors and the perpendicular bisectors meet at D in such a way that CD = 2DE.

The radius of the inscribed circle is
units, and the radius of the circumscribed circle is
units.

Answer 1

Answer:

DE = radius of the inscribed circle =  a/2√3

CD = radius of the circumscribed circle = a/√3

Step-by-step explanation:

Triangle ABC is an equilateral triangle. The angle bisectors and the perpendicular bisectors meet at D in such a way that CD = 2DE.

The angle bisectors and the perpendicular bisector are same in equilateral triangle

CE = √3 a / 2   where a is side of equilateral triangle

CD + DE = CE

2DE + DE = CE

=> 3DE = CE

=> DE = CE/3

=> DE = (√3 a / 2 )/3

=> DE = a/2√3

CD = 2  * (a/2√3)

=> CD = a/√3

DE = radius of the inscribed circle=  a/2√3

CD = radius of the circumscribed circle =  a/2√3