If the lines shown in the picture touch the circle only at points A an

Yes you are right..
Because we know AC and AO, we will know CO..add the radius and we can get our answer..
\(\sqrt{9^2+5^2}\)+5

Hi chetan2u,

I am unable to get this question!

It says maximum distance, so it has to be either A or B cos they intersect the circle at one point.

First statement gives u Radius but you are not sure cos length of hypotenuse can be anything not necessarily 13(5-12-13 triangle).
Insuff.

Second says
AC =9 units but we know nothing about CB.
Insuff.

Now, taking them together,
Radius=5, AC=9 cms, therefore, Hypotenuse=SQRT(81+25)=SQRT(106)=10.Something

But we still dont know anything about B.

what if point C is positioned more towards B or A.

Values wont be same, so we wont be able to answer the question the MAXIMUM distance between C and either A or B.

So both are insuff. thus E

I hope i was able to explain my doubt!

Looking forward to your explanation. chetan2u

honneeey,
Some info on the figure..
1) C makes tangent at A and B and will be at equidistant from A and B, so AC=BC
2) when you join a tangent with centre it makes 90° angle, so here AO will make 90° with AC ... So ACO is a right angled triangle
3) when you draw a bisector of angle BCA, it will pass through centre O and will be the longest distance.. so CD will be the longest distance..

Statement I..
This gives us radius. But we do not know CO
Insufficient
Statement II
This gives us AC, but we do not know radius.

Combined..
Triangle ACO... CO^2=AC^2+AO^2=√(9^2+5^2)=√104
Now CD=CO+OD=(√104)+5
Suff