turkey-yks 2018 Q34

turkey-yks · Other · yks-ayt Circles Optimization on a Circle
In the Cartesian coordinate plane, two circles with one centered at $(12,0)$ and the other centered at $(0,9)$ intersect only at point $(4,6)$.
What is the distance between the points on these circles that are closest to the origin?
A) $\sqrt { 5 }$ B) $\sqrt { 10 }$ C) $\sqrt { 13 }$ D) $2 \sqrt { 5 }$ E) $2 \sqrt { 10 }$
In the Cartesian coordinate plane, two circles with one centered at $(12,0)$ and the other centered at $(0,9)$ intersect only at point $(4,6)$.

What is the distance between the points on these circles that are closest to the origin?

A) $\sqrt { 5 }$
B) $\sqrt { 10 }$
C) $\sqrt { 13 }$
D) $2 \sqrt { 5 }$
E) $2 \sqrt { 10 }$