The maximum spread angle theorem is: Miller Theorem: It is known that point AB is two fixed points ON the edge ON of ∠MON and point C is a fixed point on the edge OM, then ∠ACB is maximum if and only if the outer circle of triangle ABC is tangent to the edge OM.

Miller problem: Given that point A and point B are two fixed points ON the edge ON of ∠MON, and point C is the fixed point on the edge OM, where is the maximum ∠ACB? In the process of investigating the maximum value of junior high school, Miller's problem has also become the problem of maximum opening angle or maximum perspective.

Proof: Let it be any point on the edge OM different from point C, connecting A and B, because ∠AB is the outer corner of the circle and ∠ACB is the corner of the circle, it is easy to prove that ∠AB is smaller than ∠ACB, so ∠ACB is the largest.

The problem of maximum visual angle frequently appears in mathematics competitions, previous college entrance examinations and simulation examinations, and is often examined in the background of analytic geometry, plane geometry and practical application.

If we can dig out the hidden Miller problem model from the problem setting and directly use Miller theorem to solve the problem, we will break through the bottleneck of thinking, greatly reduce the amount of calculation, reduce the difficulty of thinking and shorten the length of solving the problem, so as to solve the problem smoothly. Otherwise, this kind of problem will become a difficult problem for candidates and even be at a loss, even if it is solved, it will be time-consuming and laborious.