The circle with center C shown above is tangent to both axes. If the distance from O to C is equal to k, what is the radius of the circle, in terms of k ?


(A) k
(B) k/(sqrt 2)
(C) k/(sqrt 3)
(D) k/2
(E) k/3

Can anyone help me with this question? I understand the answer but the answer I originally got was not in the answer choices.

What I did was I extended k past the center of the circle, so I form the circle inscribed in a square.

As k is double the length, I made it so its 2k as the hypotenuse. The ratio formula for an equilateral right triangle is x : x : x*sqrt 2
So I did x*sqrt 2 = 2k
Isolate x and you get x = 2k/(sqrt 2)

So the legs of the triangle is 2k/(sqrt 2). I simplified it by multiplying both numerator and denominator by sqrt 2, so I got
X = (2k*sqrt 2)/2 which becomes k*sqrt 2. Since the leg is the diameter, I divided it by 2 and my final answer was (k*sqrt 2)/2 but the answer choice isn't there.

Is it wrong to simplify 2k/(sqrt 2)? Because if I get 2k/sqrt 2 divided by 2, then I get the correct answer. I guess my question is when do you leave the sqrt denominator alone and when do you multiply both numerator and denominator by the sqrt?