Let $ABCD$ be a convex quadrilateral in which $AC = BD$,$AB = CD$,$\angle BAC = 70^{\circ}$ and $\angle BCD = 60^{\circ}$. The acute angle between $AC$ and $BD$ is (in $^{\circ}$)

Consider the set of all triangles $OPQ$ where $O$ is the origin and $P, Q$ are distinct points in the plane with non-negative integral coordinates $(x, y)$ such that $5x + y = 99$. The number of such distinct triangles whose area is a positive integer is:

The sides of a triangle are $3x+2y-6=0$,$2x-3y+6=0$,and $x+2y+2=0$. If $P(0, b)$ lies either on the triangle or inside the triangle,then $b$ lies in the interval

Suppose the vertices of a triangle are given by $A(0,3)$,$B(-2,0)$,and $C(6,1)$. For the point $(\alpha, \alpha+1)$ to lie inside the triangle,$\alpha$ must lie in the interval:

The points $A(-4, -1)$,$B(-2, -4)$,$C(4, 0)$,and $D(2, 3)$ are the vertices of:

The incentre of the triangle formed by the lines $x+y=1$,$x=1$,and $y=1$ is