The triangle $PQR$ is inscribed in the circle ${x^2} + {y^2} = 25$. If $Q$ and $R$ have co-ordinates $(3,4)$ and $(-4, 3)$ respectively, then $\angle QPR$ is equal to
$\frac{\pi }{2}$
$\frac{\pi }{3}$
$\frac{\pi }{4}$
$\frac{\pi }{6}$
Two sides of a rhombus are along the lines, $x -y+ 1 = 0$ and $7x-y-5 =0.$ If its diagonals intersect at $(-1,-2),$ then which one of the following is a vertex of this rhombus?
In the triangle $ABC$ with vertices $A$$(2,3), B(4,-1)$ and $C(1,2),$ find the equation and length of altitude from the vertex $A$.
The equation of the line which makes right angled triangle with axes whose area is $6$ sq. units and whose hypotenuse is of $5$ units, is