In a non-right-angled triangle $$\Delta $$PQR, let p, q, r denote the lengths of the sides opposite to the angles At P, Q, R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at E, and RS and PE intersect at O. If p = $${\sqrt 3 }$$, q = 1, and the radius of the circumcircle of the $$\Delta $$PQR equals 1, then which of the following options is/are correct?

In a triangle $$\Delta $$$$XYZ$$, let $$x, y, z$$ be the lengths of sides opposite to the angles $$X, Y, Z$$ respectively, and $$2s = x + y + z$$.
If $${{s - x} \over 4} = {{s - y} \over 3} = {{s - z} \over 2}$$ and area of incircle of the triangle $$XYZ$$ is $${{8\pi } \over 3}$$, then

In a triangle $$PQR$$, $$P$$ is the largest angle and $$\cos P = {1 \over 3}$$. Further the incircle of the triangle touches the sides $$PQ$$, $$QR$$ and $$RP$$ at $$N,L$$ and $$M$$ respectively, such that the lengths of $$PN, QL$$ and $$RM$$ are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)

In $$\Delta ABC$$, internal angle bisector of $$\angle A$$ meets side $$BC$$ in $$D$$. $$DE \bot AD$$ meets $$AC$$ in $$E$$ and $$AB$$ in $$F$$. Then