A) \[\frac{3a}{4}\]
B) \[\frac{3a}{2}\]
C) \[\frac{1}{2}a\]
D) \[a\]
Correct Answer: A
Solution :
Here, \[PX=a\] \[OP=r\] and \[AX=\frac{a}{2}\] Since PX is a tangent \[\therefore \] \[\angle OPX={{90}^{o}}\] \[\therefore \] \[O{{P}^{2}}+P{{X}^{2}}=O{{X}^{2}}\] or \[{{r}^{2}}+{{a}^{2}}={{\left( r+\frac{a}{2} \right)}^{2}}\] or \[{{r}^{2}}+{{a}^{2}}={{r}^{2}}+\frac{{{a}^{2}}}{4}+ar\] or \[ar=\frac{3{{a}^{2}}}{4}\] or \[r=\frac{3a}{4}\]You need to login to perform this action.
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