If in a parallelogram $ABDC$,the coordinates of $A, B$ and $C$ are respectively $(1, 2), (3, 4)$ and $(2, 5)$,then the equation of the diagonal $AD$ is

In a triangle $ABC$,$\angle BAC = 90^{\circ}$; $AD$ is the altitude from $A$ onto $BC$. Draw $DE$ perpendicular to $AC$ and $DF$ perpendicular to $AB$. Suppose $AB = 15$ and $BC = 25$. Then the length of $EF$ is

Let $ABC$ be a triangle with $A(-3, 1)$ and $\angle ACB = \theta$,where $0 < \theta < \frac{\pi}{2}$. If the equation of the median through $B$ is $2x + y - 3 = 0$ and the equation of the angle bisector of $C$ is $7x - 4y - 1 = 0$,then $\tan \theta$ is equal to:

In a $\triangle ABC$,$2x+3y+1=0$ and $x+2y-12=0$ are the perpendicular bisectors of its sides $AB$ and $AC$ respectively. If $A$ is $(3,2)$,then the slope of the side $BC$ is

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

$(0, -1)$ and $(0, 3)$ are two opposite vertices of a square. The other two vertices are