The diameter of a circle is $AB$ and $C$ is another point on the circle. Then the area of triangle $ABC$ will be:

The area (in square units) of the circle which touches the lines $4x + 3y = 15$ and $4x + 3y = 5$ 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.

If a point $P$ has coordinates $(0, -2)$ and $Q$ is any point on the circle $x^2 + y^2 - 5x - y + 5 = 0$,then the maximum value of $(PQ)^2$ is

For the two circles $x^2 + y^2 = 16$ and $x^2 + y^2 - 2y = 0$,there is/are:

Two circles each of radius $5 \text{ units}$ touch each other at the point $(1, 2)$. If the equation of their common tangent is $4x + 3y = 10$,and $C_{1}(\alpha, \beta)$ and $C_{2}(\gamma, \delta)$,$C_{1} \neq C_{2}$ are their centres,then $|(\alpha + \beta)(\gamma + \delta)|$ is equal to .... .