How the Angle Bisector Calculator Works
This Angle Bisector Calculator uses coordinate geometry and the Angle Bisector Theorem to find where the internal angle bisector from vertex A meets side BC.
In a triangle, an angle bisector divides an angle into two equal angles. The point where the bisector from A meets side BC divides BC in the same ratio as the adjacent sides AB and AC.
Angle Bisector Theorem
If the angle bisector from A meets side BC at point P, then:
This ratio lets us calculate point P on the segment between B and C.
Coordinate Formula
If A = (xA, yA), B = (xB, yB), and C = (xC, yC), first calculate:
Then the angle bisector point P on BC is:
In coordinates:
How to Use the Calculator
- Enter the x and y coordinates of vertex A.
- Enter the x and y coordinates of vertex B.
- Enter the x and y coordinates of vertex C.
- Click calculate to find the angle bisector intersection point P on side BC.
Example Calculation
For triangle A(0,0), B(4,0), and C(2,3):
- AB = 4
- AC = √13 ≈ 3.6056
The angle bisector point on BC is:
This gives approximately:
Important Assumptions
- The three points must form a valid triangle.
- The calculator finds the internal angle bisector from vertex A.
- The result point lies on side BC.
- Coordinates are assumed to be in a 2D Cartesian plane.
Frequently Asked Questions
What is an angle bisector?
An angle bisector is a line or ray that divides an angle into two equal angles.
What does this calculator find?
It finds the point where the angle bisector from vertex A intersects side BC of the triangle.
What is the Angle Bisector Theorem?
The theorem says that an angle bisector divides the opposite side in the same ratio as the adjacent sides of the triangle.
Can the calculator find bisectors from B or C?
This version calculates the angle bisector from A. To calculate from another vertex, rename the coordinates so the desired vertex is entered as A.
What happens if the points are collinear?
If the points are collinear, they do not form a triangle, so the calculator will return an error.