.: Angle bisector :.

Angle bisector:
Ray that divides the angle in two even parts.
ray(O,C) : ang(BOC)=ang(COA)

Resume Details Construction

Resume
We will build a angle bisector of an angle defined by the rays OA and OB, as shown on the image below.

Briefly the algorithm is:
given the rays OA and OB
1: s0:= Ray ( O,A )
2: B:= Point ( 254.0,-145.0 )
3: s1:= Ray ( O,B )
4: c0:= Circunference ( O,A )
5: C:= PointIntersection_south ( s1,c0 )
6: c1:= Circunference ( A,C )
7: c2:= Circunference ( C,A )
8: E:= PointIntersection_north ( c1,c2 )
9: s2:= Ray ( O,E )

Construction's Details
  1. Build the circunference c0 of center O that passes by A.

  2. Build the intersection point between c0 and the ray OB.

  3. Build the circunference c1 of center A that passes by C, and c2, of center C that passes by A.

  4. Build the point E, intersection between c1 and c2.

  5. Build the ray OE, this ray represents the angle bisector.

Interactive construction

We present below the construction proposed above inside iGeom.

Mode the point A (or B, or O) and observe that the line s2, is always the angle bisector of AOB.

To move a point, the button "move" must be selected .