Let s ( F ) s(F) denote the set of functions subordinate to a univalent function F F in Δ \Delta the unit disk. Let B 0 {B_0} denote the set of functions ϕ ( z ) \phi (z) analytic in Δ \Delta satisfying | ϕ ( z ) | > 1 |\phi (z)| > 1 and ϕ ( 0 ) = 0 \phi (0) = 0 . We prove that if f = F ∘ ϕ f = F \circ \phi is an extreme point of s ( F ) s(F) , then ϕ \phi is an extreme point of B 0 {B_0} . Let D = F ( s ) D = F(s) and λ ( w , ∂ D ) \lambda (w,\,\partial D) denote the distance between w w and ∂ D \partial D (boundary of D D ). We also prove that if ϕ \phi is an extreme point of B 0 {B_0} and | ϕ ( e i t ) | > 1 |\phi ({e^{it}})| > 1 for almost all t t , then ∫ 0 2 π log ⁡ λ ( F ( ϕ ( e i t ) e i θ ) , ∂ D ) d t = − ∞ \int _0^{2\pi } {\log \lambda (F(\phi ({e^{it}}){e^{i\theta }}),\,\partial D)\,dt = - \infty } for almost all θ \theta .