RO-NMO 2003 Problem 103

Let be a circumcircle of radius $1$ of a triangle whose centered representation in the complex plane is given by the affixes of $a,b,c,$ and for which the equation $a+b\cos x +c\sin x=0$ has a real root in $\left( 0,\frac{\pi }{2} \right) .$ prove that the area of the triangle is a real number from the interval $\left( 1,\frac{1+\sqrt 2}{2} \right] .$ Gheorghe Iurea