The angle between the circles $x^2+y^2-2x-9=0$ and $x^2+y^2-4y-1=0$ at their point of intersection is

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.

Three circles of radii $a, b, c$ $(a < b < c)$ touch each other externally. If they have the $x$-axis as a common tangent,then:

Let $A, B, C$ be three points on a circle of radius $1$ such that $\angle ACB = \frac{\pi}{4}$. Then,the length of the side $AB$ is

The centre of the smallest circle touching the circles $x^2 + y^2 - 2y - 3 = 0$ and $x^2 + y^2 - 8x - 18y + 93 = 0$ is:

In an acute-angled $\triangle ABC$,the altitudes from $A, B, C$ when extended intersect the circumcircle again at points $A_1, B_1, C_1$ respectively. If $\angle ABC = 45^{\circ}$,then $\angle A_1 B_1 C_1$ equals (in $^{\circ}$)