Triangle Angle Bisector Calculator
Angle Bisector from A: - units
Angle Bisector from B: - units
Angle Bisector from C: - units
Understanding Triangle Angle Bisectors
What is an Angle Bisector?
An angle bisector is a line that divides an angle into two equal parts. In a triangle, each angle has a unique bisector that extends to the opposite side.
Angle Bisector Length (from vertex A) = 2bc cos(A/2)/(b+c)
where:
- b, c are adjacent sides
- A is the angle being bisected
- cos(A/2) = √[(s(s-a))/bc]
- s = (a+b+c)/2 (semi-perimeter)
Properties of Angle Bisectors
- Concurrent Lines: All three angle bisectors meet at the incenter
- Incenter: Equidistant from all sides
- Ratio Property: Divides opposite side proportionally
- Internal Division: Bisector divides opposite side internally
- Circle Property: Inscribed circle tangent points
- Angular Relations: Equal angles on either side
- Distance Property: Points on bisector equidistant from sides
- Area Relations: Creates proportional areas
Advanced Concepts and Applications
Euclidean Geometry
Fundamental construction
Trigonometry
Angular relationships
Engineering
Structural design
Architecture
Geometric patterns
Computer Graphics
Ray tracing algorithms
Optimization
Shortest path problems