<Tri-2025-2241>, hint

Suppose GP cut AB at P' such that AP'/P'B=t/(1-t), GP'=t GB+(1-t)GA=tb+(1-t)a

The line through P' parallel to AD cut BC in A', parallel to BE cuts AC in B', parallel to CF 

cut AB in C'.  DA'=t(b+a/2), EB'=(1-t)(a+b/2), FP'=(a-b)(1/2-t)

Hence DA'+EB'+FP'=3/2 [tb+(1-t)a]=3/2 GP'