Editing Thales's theorem (section)

==Generalizations and related results==
As stated above, Thales's theorem is a special case of the [[inscribed angle theorem]] (the proof of which is quite similar to the first proof of Thales's theorem given above):
:Given three points {{mvar|A}}, {{mvar|B}} and {{mvar|C}} on a circle with center {{mvar|O}}, the angle {{math|∠ ''AOC''}} is twice as large as the angle {{math|∠ ''ABC''}}.
A related result to Thales's theorem is the following:

*If {{mvar|{{overline|AC}}}} is a diameter of a circle, then:
:*If {{mvar|B}} is inside the circle, then {{math|∠ ''ABC'' > 90°}}
:*If {{mvar|B}} is on the circle, then {{math|1=∠ ''ABC'' = 90°}}
:*If {{mvar|B}} is outside the circle, then {{math|∠ ''ABC'' < 90°}}.