Can two circles intersect each other at right angles, such that one circle passes through the center of the other circle? More precisely, do there exist two intersecting circles such that the tangent lines at the intersection points make an angle of 90 degrees, and one of the circles passes through the center of the other? I think the answer is no, and that this can only be the case if the circle passing through the center of the other circle is actually a line. I'm not sure how to show this though. Can someone give a proof or a counterexample?

If circle $C_2$ passes through the center of circle $C_1$ then the line passing through the center of $C_1$ and the intersection point of the circles intersects $C_1$ at a right angle.
On the other hand, that line is a secant line for $C_2$ and therefore not tangential to $C_2$.

