$A$ line $L_1$ passing through $A(3,4)$ and having slope $1$ cuts another line $L_2$ passing through $C$ at $B$,such that $AB = AC$. If the equation of line $BC$ is $2x - y + 4 = 0$,then the equation of $AC$ is

The triangle formed by joining the points $P(2, 7)$,$Q(4, -1)$,and $R(-2, 6)$ is:

Let $A, B$ be points on the two half-lines $x - \sqrt{3}|y| = \alpha, \alpha > 0$ at a distance of $\alpha$ from their point of intersection $P$. The line segment $AB$ meets the angle bisector of the given half-lines at the point $Q$. If $PQ = \frac{9}{2}$ and $R$ is the radius of the circumcircle of $\triangle PAB$, then $\frac{\alpha^2}{R}$ is equal to . . . . . .

$A$ vertex of an equilateral triangle is $(2, 3)$ and the equation of the opposite side is $x + y = 2$. Then,the equation of one of the other two sides is:

The perimeter of a triangle is $16 \text{ cm}$, one of the sides is of length $6 \text{ cm}$. If the area of the triangle is $12 \text{ cm}^2$, then the triangle is:

Suppose the hypotenuse and its opposite vertex of an isosceles right-angled triangle are $3x + 4y - 4 = 0$ and $(2, 2)$ respectively. Then,which of the following is another side of the triangle?