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Mathematics circle of grade three
The truth is that "the outer angle of the circle opposite to the same arc in the circle is greater than the circumferential angle." Let p be a point outside the circle, connecting XP, YP and ZP. Obviously, there is ∠XZY=∠X+∠Y+∠XPY according to the fact that the △ outer angle is equal to the sum of the non-adjacent inner angles, so when P is out of the circle, there is always ∠XPY < ∠XZY, and vice versa.