Let C be a circle with centre P₀and AB be a diameter of C. Suppose P₁is the mid point of the line segment P₀B, P₂is the mid point of the line segment P₁B and so on. Let C₁, C₂, C₃, ...... be circles with diameters P₀P₁, P₁P₂, P₂P₃... respectively. Suppose the circles C_1,C₂, C₃, .... are all shaded. The ratio of the area of the unshaded portion of C to that of the original circle C is?

The lines represented by the three equations

 2X+3Y-5=0: 3X-5Y+2=0, and -5X+2Y+3=0

In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If Angle CBE = 65 degree, then what is the value of DEC?