Are you using the free version?
GPT 4 Turbo (which is paid) gives this:
> Lexell's theorem is a result in geometry related to triangles and circles. Named after the mathematician Anders Johan Lexell, the theorem describes a special relationship between a triangle and a circle inscribed in one of its angles. Here's the theorem:
Given a triangle \(ABC\) and a circle that passes through \(B\) and \(C\) and is tangent to one of the sides of the angle at \(A\) (say \(AB\)), the theorem states that the circle's other tangent point with \(AB\) will lie on the circumcircle of triangle \(ABC\).
In other words, if you have a circle that touches two sides of a triangle and passes through the other two vertices, the point where the circle touches the third side externally will always lie on the triangle’s circumcircle. This theorem is useful in solving various geometric problems involving circles and triangles.
> Lexell's theorem is a result in geometry related to triangles and circles. Named after the mathematician Anders Johan Lexell, the theorem describes a special relationship between a triangle and a circle inscribed in one of its angles. Here's the theorem:
Given a triangle \(ABC\) and a circle that passes through \(B\) and \(C\) and is tangent to one of the sides of the angle at \(A\) (say \(AB\)), the theorem states that the circle's other tangent point with \(AB\) will lie on the circumcircle of triangle \(ABC\).
In other words, if you have a circle that touches two sides of a triangle and passes through the other two vertices, the point where the circle touches the third side externally will always lie on the triangle’s circumcircle. This theorem is useful in solving various geometric problems involving circles and triangles.