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.
Correct Answer: B
Solution :
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.You need to login to perform this action.
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