A) Statement-1 and 2 are true and Statement-2 is correct explanation of Statement-1.
B) Statement-1 and 2 are true and Statement-2 is not correct explanation of Statement-1.
C) Statement-1 is true, statement-2 is false.
D) Statement-1 is false, Statement-2 is true.
Correct Answer: D
Solution :
Let centres of the circles be \[{{C}_{1}}\]and \[{{C}_{2}}\] \[\Rightarrow \]\[{{C}_{1}}\,\text{is}\,(\sqrt{1-2a,}a){{C}_{2}}\,\text{is}\,(\sqrt{1-2b},b)\] \[\Rightarrow \]\[{{C}_{1}}{{C}_{2}}=a+b=a+\frac{1}{2}\] \[\Rightarrow \]\[1-2a+{{\left( a-\frac{1}{2} \right)}^{2}}={{\left( a+\frac{1}{2} \right)}^{2}}\] \[\Rightarrow \]\[a=\frac{1}{4}.\]You need to login to perform this action.
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