Which equation of the chord bisects the circle $x^2 + y^2 = 8x$ at the point $(4, 3)$?

Consider a semicircle of radius $1$ unit constructed on the diameter $AB$ and let $O$ be its centre. Let $C$ be a point on $AO$ such that $AC:CO = 2:1$. Draw $CD$ perpendicular to $AO$ with $D$ on the semicircle. Draw $OE$ perpendicular to $AD$ with $E$ on $AD$. Let $OE$ and $CD$ intersect at $H$. Then,$DH$ equals

The acute angle between the curves $x^2+y^2=x+y$ and $x^2+y^2=2y$ is

$A$ circle touching the $x-$ axis at $(3, 0)$ and making an intercept of length $8$ on the $y-$ axis passes through the point:

If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ touches the $x$-axis,then:

The least distance of the point $A(10, 7)$ from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ is the length of segment $AM$. If $MM'$ is the diameter of the circle,then the lengths of $AM$ and $AM'$ are respectively . . . . . . , . . . . . . units.