Mathematics - Straight Lines Question with Solution | TestHub

The intersection point of the given diagonals is $\mathrm{P}\equiv \left(\frac{3}{2},5\right)$. Equations of angular bisectors of the diagonals are $\frac{y+8x-17}{\sqrt{65}}=\pm \frac{y-8x+7}{\sqrt{65}}\Rightarrow x=\frac{3}{2}$ and $y=5$. Let length of BC be $a$ and that of CD be $b$. Then $\tan \theta =\frac{a/2}{b/2}=\frac{a}{b}=8$. Also $ab=8\Rightarrow a=8,b=1$. So equations of sides are $y=1,y=9,x=1$ and $x=2$.