Question

In ABC, the angle bisectors meet at point D. Point E is on AC, and DE is perpendicular to AC. Point F is the location where the perpendicular bisectors of the sides of the triangle meet. What is the radius of the largest circle that can fit inside ABC?

Answer 1

@Hero @Michele_Laino

Answer 2

@ash2326

Answer 3

????

Answer 4

hint:
The bisector of an angle is the set of all points whose distance from the sides of the angle which they refer to, are the same. Furthermore the segment DE is perpendicular to AC