Olympiad geometry question

[UWU11]

Let ABC be a non-equilateral triangle and ω be an inscribed circle of triangle ABC, which touch sides BC, AC and AB at the points D, E, and F, respectively. Let G be the point on the circle ω such that ∠AGD = 90◦.
If DG and EF intersect at point P, prove that AP is parallel to BC.

I’m trying to prove that ∠ACB=∠PAC but I have no idea how to start.

 

[blamocur]

Let ABC be a non-equilateral triangle and ω be an inscribed circle of triangle ABC, which touch sides BC, AC and AB at the points D, E, and F, respectively. Let G be the point on the circle ω such that ∠AGD = 90◦.
If DG and EF intersect at point P, prove that AP is parallel to BC.

I’m trying to prove that ∠ACB=∠PAC but I have no idea how to start.

Start with making a neat drawing.