Question

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. $\frac{k}{\sqrt{2}}$
• C. $\frac{k}{\sqrt{3}}$
• D. $\frac{k}{2}$
• E. $\frac{k}{3}$

Answer 1

The correct option is B $\frac{k}{\sqrt{2}}$

Let $r$ be radius of the circle.

Since tangent is perpendicular to radius at point of contact, the shown triangle is right angled.

Since $OC=k,$; by Pythagoras theorem applied to the right triangle,

then $r^2+r^2=k^2$

$r=\frac{k}{\sqrt{2}}$

option B is the answer.