Names of two circle theorems in English [closed]

Question

There are two theorems:

1. All three angles AC_1B, AC_2B, AC_3B are equal. In general: All angles above a chord are equal.
2. The size of any angle above a chord AB is half the size of angle AOB where O is the center of the circle.

I am Czech. In my native language there is a name of both these two statements separately.

1. věta o obvodovém úhlu
2. věta o středovém úhlu

What are these two theorems called in English?

Thank you.

Answer 1

The inscribed angle theorem. Sometimes known as the Star Trek Lemma. A generalization of Thale's Theorem.

 

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