Question

HELP PLSSSSS 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

CE = CD + DE = 2DE + DE = 3DE = 8.7

DE = 8.7/3 = 2.9
CD = 2DE = 5.8

For the inscribed circle, where center is point D. The radius is length DE.
This is because the circle will touch the 3 points where the bisectors intersect with sides of triangle.
radius = 2.9

For circumscribed circle, the center will also be point D. The radius is CD.
The circle will touch 3 points of triangle, A,B,C.
radius = 5.8