We propose a novel minimal solver for sphere fitting via its 2D central projection, i.e., a special ellipse. The input of the presented algorithm consists of contour points detected in a camera image. General ellipse fitting problems require five contour points. However, taking advantage of the isotropic spherical target, three points are enough to define the tangent cone parameters of the sphere. This yields the sought ellipse parameters. Similarly, the sphere center can be estimated from the cone if the radius is known. These proposed geometric methods are rapid, numerically stable, and easy to implement. Experimental results—on synthetic, photorealistic, and real images—showcase the superiority of the proposed solutions to the state-of-the-art methods. A real-world LiDAR-camera calibration application justifies the utility of the sphere-based approach resulting in an error below a few centimeters.