Let O be the origin and OP and OQ be the tangents to the circle $$x^2+y^2-6x+4y+8=0$$ at the points P and Q on it. If the circumcircle of the triangle OPQ passes through the point $$\left( {\alpha ,{1 \over 2}} \right)$$, then a value of $$\alpha$$ is :

If the tangents at the points $$\mathrm{P}$$ and $$\mathrm{Q}$$ on the circle $$x^{2}+y^{2}-2 x+y=5$$ meet at the point $$R\left(\frac{9}{4}, 2\right)$$, then the area of the triangle $$\mathrm{PQR}$$ is :

Let a circle $$C_{1}$$ be obtained on rolling the circle $$x^{2}+y^{2}-4 x-6 y+11=0$$ upwards 4 units on the tangent $$\mathrm{T}$$ to it at the point $$(3,2)$$. Let $$C_{2}$$ be the image of $$C_{1}$$ in $$\mathrm{T}$$. Let $$A$$ and $$B$$ be the centers of circles $$C_{1}$$ and $$C_{2}$$ respectively, and $$M$$ and $$N$$ be respectively the feet of perpendiculars drawn from $$A$$ and $$B$$ on the $$x$$-axis. Then the area of the trapezium AMNB is :