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

$A$ straight line through the vertex $P$ of a triangle $PQR$ intersects the side $QR$ at the point $S$ and the circumcircle of the triangle $PQR$ at the point $T$. If $S$ is not the centre of the circumcircle,then:
$(A) \frac{1}{PS}+\frac{1}{ST}<\frac{2}{\sqrt{QS \times SR}}$
$(B) \frac{1}{PS}+\frac{1}{ST}>\frac{2}{\sqrt{QS \times SR}}$
$(C) \frac{1}{PS}+\frac{1}{ST}<\frac{4}{QR}$
$(D) \frac{1}{PS}+\frac{1}{ST}>\frac{4}{QR}$

The circles $x^2 + y^2 - 10x + 16 = 0$ and $x^2 + y^2 = r^2$ intersect each other in two distinct points,if

The number of common tangents to the circles $x^2+y^2-2x-6y+9=0$ and $x^2+y^2+6x-2y+1=0$ is

The radius of the circle having three chords along the $y$-axis,the line $y=x$,and the line $2x+3y=10$ is

If the lines $12x - 5y - 17 = 0$ and $24x - 10y + 44 = 0$ are tangents to the same circle,then the radius of the circle is: