Six consecutive sides of an equiangular octagon are $6, 9, 8, 7, 10, 5$ in that order. The integer nearest to the sum of the remaining two sides is

If one side of an isosceles triangle is given by the line $y=2$ and the base is provided by the points $(2,0)$ and $(0,2)$,then its area (in sq. units) is

The area (in square units) of the triangle formed by the lines $x=0, y=0$ and $3x+4y=12$ is:

Let the mirror image of point $A(\alpha, \beta)$ in the line mirror $x + 2y = 3$ be point $B$,and the image of $B$ in the line $3x - 2y = 5$ be $C$. If the origin is the orthocentre of triangle $ABC$ and $P(a, b)$ is a point inside the triangle such that triangles $PAB$,$PBC$,and $PCA$ have the same area,then $3(a + b)$ is:

If the sum of the distances of a point from two perpendicular lines in a plane is $1$,then its locus is

If the lines $3x + y - 4 = 0$,$x - ay - 10 = 0$,and $bx + 2y + 9 = 0$ form three successive sides of a rectangle in that order and the fourth side passes through $(1, 2)$,then the area of that rectangle (in sq. units) is