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 $AB$ be a line segment with mid-point $C$ and $D$ be the mid-point of $AC$. Let $C_1$ be the circle with diameter $AB$ and $C_2$ be the circle with diameter $AC$. Let $E$ be a point on $C_1$ such that $EC$ is perpendicular to $AB$. Let $F$ be a point on $C_2$ such that $DF$ is perpendicular to $AB$ and $E$ and $F$ lie on opposite sides of $AB$. Then,the value of $\sin \angle FEC$ is

The radical center of the three circles described with the three sides of a triangle as diameters is:

Three circles of radii $1, 2$ and $3$ units respectively touch each other externally in the plane. The circumradius of the triangle formed by joining the centers of the circles is

If the straight line $y=mx$ lies outside of the circle $x^2+y^2-20y+90=0$,then the value of $m$ will satisfy

If the chord $x+y=1$ of the circle $x^2+y^2=a^2$ subtends a right angle at the origin,then $a=$