Given the equilateral triangle ABC, the bisectors of angle B and angle c intersect at O, the vertical bisectors of Bo and co intersect at e f respectively, can you get be = EF = FC?

Given the equilateral triangle ABC, the bisectors of angle B and angle c intersect at O, the vertical bisectors of Bo and co intersect at e f respectively, can you get be = EF = FC?

sure
Firstly, we connect EO and fo, because they are vertical bisectors, we can get BeO and CFO are isosceles triangle
So be = EO CF = fo
Because ABC is an equilateral triangle, Bo and Co are bisectors
Therefore, OBE = BOE = FOC = OCF = 30 degree
Therefore, OEF = ofe = 60 degree
So the triangle OEF is an equilateral triangle
So OE = of = EF
Because be = EO, CF = fo (before)
So be = EF = FC (there are other ways to calculate the length, you can try it yourself)
I haven't studied mathematics for several years. I'm not very professional. Please forgive me