The number of circles that touch all the three lines $x+y-1=0$,$x-y-1=0$,and $y+1=0$ is

$A$ rectangle $ABCD$ is inscribed in a circle whose center lies on the line $3y = x + 10$. If $A$ and $B$ are the points $(-6, 7)$ and $(4, 7)$ respectively,find the area of the rectangle.

If the line $x - y + 1 = 0$ is a chord of the circle $x^2 + y^2 + 4y - 4 = 0$,find the length of this chord.

The equation of the chord of the circle $x^2 + y^2 = a^2$ having $(x_1, y_1)$ as its mid-point is

Let $PQ$ and $RS$ be tangents at the extremities of a diameter $PR$ of a circle of radius $r$ such that $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle,then $2r$ equals

If a circle $C_1: x^2+y^2=16$ intersects another circle $C_2$ with radius $5$ such that the common chord is of maximum length and has a slope equal to $\frac{3}{4}$,then the centre of the circle $C_2$ is