DIRECTION: Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (ONLY ONE option is correct) from the following- |
Let \[C\] be a circle with centre \[O\] and \[HK\] is the chord of contact of pair of the tangents from points \[A\]. \[OA\] intersects the circle \[C\] at \[P\] and \[Q\] and \[B\] is the midpoint of \[HK\], then |
Statement-1: \[AB\] is the harmonic mean of \[AP\] and \[A\] because |
Statement-2: \[AK\] is the Geometric mean of \[AB\] and\[AO,\,\,\,OA\] is the arithmetic mean of \[AP\] and \[A\] |
A) Statement-1 is false, Statement-2 is true.
B) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
C) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
D) Statement-1 is true, Statement-2 is false.
Correct Answer: B
Solution :
\[\frac{(AK)}{(OA)}=\cos \theta =\frac{AB}{AK}\] \[\Rightarrow \] \[{{(AK)}^{2}}=(AB)(OA)=(AP)(AQ)\] ? (1) \[[A{{K}^{2}}=AP.AQ\]using power of point\[A]\] Also, \[OA=\frac{AP+AQ}{2}\] \[[AQ-AO=r=AO-AP\Rightarrow 2AO=AQ+AP]\] \[\Rightarrow \]\[(AP)(AQ)=AB\left( \frac{AP+AQ}{2} \right)\](from (1)) \[\Rightarrow \] \[AB=\frac{2(AP)(AQ)}{(AP+AQ)}\]You need to login to perform this action.
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