Prove that the intersection of a sphere in a plane is a circle.
Let $O$ be the center of the sphere, and let $\pi$ be the plane intersecting the sphere. Construct a perpendicular line from $O$ to $\pi$ and let $X$ be the point that the perpendicular line intersects on $\pi$. Now put two points on the intersection and make two triangles. This is as far as I got. I feel like if I can prove that both triangles are congruent then it proves that every point from $O$ is the same distance which implies a circle.