Which Mohr circle is correct for the given stress state

The given stress components for the stress element are,

       σ_x = 30 MPa
     σ_y = -60 MPa
     τ_xy = 50 MPa

Mohr's Circle center will be at the normal stress average,
     σ_average = [30 + (-60)]/2 = -15 MPa

which is plotted on the diagram at the left. Next, a point on the circle is needed. Two different points can be used,

     Point 1: (σ_x , τ_xy) = (30, 50)
     Point 2: (σ_y, -τ_xy) = (-60, -50)

Remember, the shear stress is plotted positive in the downward direction. From the plotted center and points on the circle, the radius (shear maximum) can be determined.

     R = τ_max = [(30+15)² + 50²]^1/2 = 67.3 MPa

Principal stresses are

     σ₁ = -15 + 67.3 = 52.3 MPa
     σ₂ = -15 - 67.3 = -82.3 MPa

The principle direction is      

tan 2θ₁ = 50/(15+30)
      2θ₁ = 48.0^o

The correct diagram is 1)