The triangle of maximum area inscribed in a circle is -

If the inverse point of the point $(3, 2)$ with respect to the circle $x^2+y^2-2x+4y-4=0$ is $(l, m)$,then $(2l+19m) =$

Let $XY$ be the diameter of a semi-circle with center $O$. Let $A$ be a variable point on the semi-circle and $B$ another point on the semi-circle such that $AB$ is parallel to $XY$. The value of $\angle BOY$ for which the inradius of $\triangle AOB$ is maximum,is

The equation of the circle with $(1,1)$ as centre and which cuts a chord of length $4 \sqrt{2}$ units on the line $x+y+1=0$ is

The line $y = x$ cuts the circle $x^2 + y^2 - 2x = 0$ at points $A$ and $B$. Find the equation of the circle having $AB$ as its diameter.

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