Which of the following statements are true and which are false? In each case,give a valid reason for your answer.
$p:$ Each radius of a circle is a chord of the circle.

Let $PQ$ be a diameter of the circle $x^{2}+y^{2}=9$. If $\alpha$ and $\beta$ are the lengths of the perpendiculars from $P$ and $Q$ on the straight line $x+y=2$ respectively,then the maximum value of $\alpha \beta$ is

The points $A(a, 0), B(0, b), C(c, 0)$ and $D(0, d)$ are such that $ac = bd$ and $a, b, c, d$ are all non-zero. Then the points:

Among the chords of the circle $x^2+y^2=75$,the number of chords having their midpoints on the line $x=8$ and having their slopes as integers is

The angle between the pair of tangents from the point $(1, 1/2)$ to the circle $x^2 + y^2 + 4x + 2y - 4 = 0$ is:

The number of tangents that can be drawn from $(0, 0)$ to the circle $x^2 + y^2 + 2x + 6y - 15 = 0$ is