Editing Thales's theorem (section)

===Alternate proof of the converse using geometry===
Given a right triangle {{mvar|ABC}} with hypotenuse {{mvar|AC}}, construct a circle {{math|Ω}} whose diameter is {{mvar|AC}}. Let {{mvar|O}} be the center of {{math|Ω}}. Let {{mvar|D}} be the intersection of {{math|Ω}} and the ray {{mvar|OB}}. By Thales's theorem, {{math|∠ ''ADC''}} is right. But then {{mvar|D}} must equal {{mvar|B}}. (If {{mvar|D}} lies inside {{math|△''ABC''}}, {{math|∠ ''ADC''}} would be obtuse, and if {{mvar|D}} lies outside {{math|△''ABC''}}, {{math|∠ ''ADC''}} would be acute.)