Question

in an equirateral triangle,prove that the centroid and the circumference of the triangle coincide

Answer 1

question inappropriate

Answer 2

(ABC are triangle vertices, DEF are midpoints on triagle sides and O is the intersection of medians)
In triangles ABD and ACD
BD= CD (by median definition)
AD= AD (common segment)
angles ABC= ACB (equlateral triangle)
results triangles ABD=ACD
results angle BAD=CAD (=60/2=30 degree)
By smilarity all angles BAD=CAD=CBE=BCF=ACF=BCF(=30 deg)
We know angle ABC=ACD=BAC (=60 deg) because the triangle is eqilateral
Results angles ADC=ADB=BEA=BEC=CFA=CFB (=90 deg)
Now the triagle is equilateral...