$(
Angle Bisector (SidePoint1, Vertex, SidePoint2)
${
An Angle Bisector that behaves exactly as the GSP construction.
The Givens are the same as for standard Angle Bisectors.
There is a small difference to the standard construction:
the bisector ray has the same position, but points on it move
as Side Point 2 is moved closer and further away from the Vertex.
In other words, the length unit on the bisector ray is equal
to the distance from the Vertex to Side Point 2.
The construction uses fewer auxiliary elements as the fully compatible one in Bisector.gss.
$}
Ray ($SidePoint1, $Vertex) [hidden];
Circle ($Vertex, $SidePoint2) [hidden];
Intersect2 ($2, $1) [hidden];
Segment ($SidePoint2, $1) [hidden];
Midpoint ($1) [hidden];
Ray ($1, $Vertex);
$)
${
Just testing.
$P1 Point (100, 50) [label ('P1')];
$P2 Point ( 50, 100) [label ('P2')];
$P3 Point (100, 150) [label ('P3')];
Ray ($P1, $P2);
Ray ($P3, $P2);
Angle Bisector ($P1, $P2, $P3) [thick];
Point on Object ($1, 1.5);
$}