Rectangles on sides of triangle

Let ABC be a triangle and BCCaBa, CAAbCb, ABBcAc three rectangles constructed on the sides of the triangle. The perpendicular bisectors of AbAc, BcBa, CaCb are concurrent.

Particular case:

If DEF is the triangle medial and the midpoints of CaBa, AbCb, BcAc are D', E' and F' such that vec[OD']=t*vec[OD], vec[OE']=t*vec[OE], vec[OF']=t*vec[OF], respectively, the perpendicular bisectors of AbAc, BcBa, CaCb concur in (on Euler line):

(-a^2(b^2 + c^2)(t-1) + 2a^4t - (b^2-c^2)^2 (1 + t) :
-a^4(1 + t) + (b^2 - c^2)(2b^2t + c^2(1 + t)) + a^2(-b^2(t-1) + 2c^2(1 + t)) :
-a^4(1+t)-(b^2-c^2)(2c^2t + b^2(1+t))+ a^2(-c^2(t-1)+2b^2(1 + t)) )