Editing Central angle (section)

==Formulas==
If the intersection points {{mvar|A}} and {{mvar|B}} of the legs of the angle with the circle form a [[diameter]], then {{math|1=Θ = 180°}} is a [[straight angle]]. (In radians, {{math|1=Θ = π}}.)

Let {{math|''L''}} be the '''minor arc''' of the circle between points {{mvar|A}} and {{mvar|B}}, and let {{mvar|R}} be the [[radius]] of the circle.<ref>{{cite web|url=http://www.mathopenref.com/circlecentral.html|title=Central angle (of a circle)| publisher =Math Open Reference|year=2009|accessdate=December 30, 2013}} interactive</ref>
[[Image:Angle central convex.svg|frame|right|Central angle. Convex. Is subtended by minor arc {{math|''L''}}]]
If the central angle {{math|Θ}} is subtended by {{math|''L''}}, then 
<math display="block"> 0^{\circ} < \Theta < 180^{\circ} \, , \,\, \Theta = \left( {\frac{180L}{\pi R}} \right) ^{\circ}=\frac{L}{R}.</math>

{{math proof|title=Proof (for degrees)|proof= The [[circumference]] of a circle with radius {{mvar|R}} is {{math|2π''R''}}, and the minor arc {{math|''L''}} is the ({{sfrac|Θ|360°}}) proportional part of the whole circumference (see [[Arc (geometry)|arc]]). So: 
<math display="block">L=\frac{\Theta}{360^{\circ}} \cdot 2 \pi R \, \Rightarrow  \, \Theta = \left( {\frac{180L}{\pi R}} \right) ^{\circ}.</math>}}

[[Image:Angle central reflex.svg|frame|right|Central angle. Reflex. Is ''not'' subtended by {{math|''L''}}]]
{{math proof|title=Proof (for radians)|proof= The [[circumference]] of a circle with radius {{mvar|R}} is {{math|2π''R''}}, and the minor arc {{math|''L''}} is the ({{sfrac|Θ|2π}}) proportional part of the whole circumference (see [[Arc (geometry)|arc]]). So
<math display="block">L=\frac{\Theta}{2 \pi} \cdot 2 \pi R \, \Rightarrow  \, \Theta = \frac{L}{R}.</math>}}

If the central angle {{math|Θ}} is '''not''' subtended by the minor arc {{math|''L''}}, then {{math|Θ}} is a reflex angle and
<math display="block"> 180^{\circ} < \Theta < 360^{\circ} \, , \,\, \Theta = \left( 360 - \frac{180L}{\pi R} \right) ^{\circ}=2\pi-\frac{L}{R}.</math>

If a tangent at {{math|''A''}} and a tangent at {{math|''B''}} intersect at the exterior point {{math|''P''}}, then denoting the center as {{math|''O''}}, the angles {{math|∠''BOA''}} (convex) and {{math|∠''BPA''}} are [[Supplementary angles|supplementary]] (sum to 180°).