• # question_answer Direction: For the following questions. Choose the correct answer from the codes [a], [b], [c] and [d] defined as follows. For each of the following questions, one out of given options is correct. Statement I lf$\frac{x}{a}+\frac{y}{b}=1$ and $\frac{x}{c}+\frac{y}{d}=-1$ cut $x$ and $y-$ axes at four concyclic points, A, B, C and D respectively, then the orthocentre of $\Delta ABC$is $\left( 0,\,\frac{ac}{b} \right)$. Statement II If chords AC and BD of a circle intersect at origin O, then$OA\cdot OC=OB\cdot OD$. A)  Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I. B)  Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I. C)  Statement I is true, Statement II is false. D)  Statement I is false. Statement II is true.

The orthocentre of $\Delta ABC$ be $H(0,\,\,\alpha )$. $\Rightarrow$            ${{m}_{CH}}\cdot {{m}_{AB}}=-1$ $\Rightarrow$            $\frac{\alpha -0}{0-(-c)}\cdot \,\frac{b-0}{0-a}=-1$ $\Rightarrow$            $b\alpha =ac$ $\Rightarrow$            $\alpha =\frac{ac}{b}$ $\therefore$ Orthocentre of $\Delta ABC$ is $H\left( 0,\,\frac{ac}{b} \right)$. Also, statement II is true but not the correct explanation for statement I.