There are a number of theorems referred to as "The Circle Theorems." Arguments abound as to which ones should be included and which ones should not. Here are some circle theorems:

Angle subtended by a diameter is 90 degrees

Thales Theorem

Angles subtended on the same arc are equal

Generalising Thales's theorem

A tangent and a radius meet at a right angle
Tangents that meet at a point are the same length
For an arc, angle subtended at the centre is double that on the circumference
Alternate angle theorem

Oppose angles in a cyclic quadrilateral add to 180 degrees.

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Circle Theorem

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