The circumradius of the triangle formed by the lines $xy+2x+2y+4=0$ and $x+y+2=0$ is

The equations $y = \pm \sqrt{3}x$ and $y = 1$ represent the sides of which triangle?

Let $ABC$ be a triangle such that the equations of lines $AB$ and $AC$ are $3y-x=2$ and $x+y=2$,respectively,and the points $B$ and $C$ lie on the $x$-axis. If $P$ is the orthocentre of the triangle $ABC$,then the area of the triangle $PBC$ is equal to

Let $m_{1}, m_{2}$ be the slopes of two adjacent sides of a square of side $a$ such that $a^{2}+11 a+3(m_{1}^{2}+m_{2}^{2})=220$. If one vertex of the square is $(10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))$,where $\alpha \in(0, \frac{\pi}{2})$ and the equation of one diagonal is $(\cos \alpha-\sin \alpha) x +(\sin \alpha+\cos \alpha) y =10$,then $72(\sin ^{4} \alpha+\cos ^{4} \alpha)+a^{2}-3 a+13$ is equal to.

If the lines $x + 3y = 4$,$3x + y = 4$,and $x + y = 0$ form a triangle,then the triangle is:

In a $\triangle ABC$,$AB = AC = 37$. Let $D$ be a point on $BC$ such that $BD = 7$ and $AD = 33$. The length of $CD$ is: