Tang's Theorem

Tang’s Theorem states that in a circle, if a triangle is inscribed such that one side is a diameter, then the angle opposite that side is a right angle (90 degrees). Conversely, if a triangle has a right angle, then its hypotenuse will be the diameter of the circle that passes through its three vertices. Essentially, it connects the concepts of right triangles and circles, showing that any right triangle can be inscribed in a circle with the hypotenuse as the diameter. This theorem is fundamental in understanding the relationship between right triangles and circle geometry.