Circles intersecting at two points orthogonally. I am finding the following much harder than it probably is!
If a circle $A$ intersects the circle $B$ at two points orthogonally, then why can't $A$ pass through the centre of B?

Let $X $ and $Y $ be the centres of $A $  and $ B $, respectively, and let $Z $ be one of the two points where those circles intersect each other. The triangle $\triangle XZY$ is a right-angled triangle with hypotenuse $XY $, thus $XY $ is the longest side of the triangle: $XY\gt XZ $ and, since $XZ $ is the radius of $A $, the point $Y $ lies outside of $A $
