Triangle Bisector Calculator: How to Calculate and Why it Matters
Bisector
A bisector is a ray emanating from the top of an angle and dividing this angle into two equal angles. You can also define the bisector as the geometrical location of the points inside the corner equidistant from the sides of this angle.
Triangle
Triangle — is a geometric figure that has three points that do not lie on the same line and three segments that pair these points in pairs. The points of a triangle are usually called its vertices, and the segments are called its sides.
Triangle bisector calculator
Intro
The bisectors of a triangle are lines that divide the interior angles of the triangle into two equal parts. These lines meet at a single point, known as the incenter, which is the center of the triangle's inscribed circle. The triangle bisector calculator allows you to quickly and easily calculate the bisectors of any triangle.
How to Calculate Triangle Bisectors
To calculate the bisectors of a triangle, follow these steps:
Through sides
 Measure the three sides of the triangle.

Use the sides to calculate the bisector for each side using the following formula: l_a = \dfrac{\sqrt{cb(a+b+c)(c+ba)}}{c+b} \\
l_b = \dfrac{\sqrt{ac(a+b+c)(a+cb)}}{a+c} \\
l_c = \dfrac{\sqrt{ab(a+b+c)(a+bc)}}{a+b}
Where:
 l_a, l_b, l_c  triangle bisectors
 a, b, c  triangle sides
Through angle and side
 Measure the three angles of the triangle using a protractor and the sides.
 Calculate the halfangle for each angle by dividing it by 2.

Use the halfangles to calculate the bisector for each angle using the following formula: l_a = \dfrac{a*sin(\frac{\gamma}{2})}{sin(90^0+\frac{\gamma}{2})} \\
l_b = \dfrac{b*sin(\frac{\beta}{2})}{sin(90^0+\frac{\beta}{2})} \\
l_c = \dfrac{c*sin(\frac{\alpha}{2})}{sin(90^0+\frac{\alpha}{2})}Where:
 l_a, l_b, l_c  triangle bisectors
 a, b, c  opposite sides to angles
 \alpha, \beta, \gamma  triangle angles
Right triangle, through sides
 Measure the two sidess of the triangle.

Use the sides to calculate the bisector using the following formula: l = \sqrt{2}\dfrac{ac}{a+c}Where:
 l  triangle bisector
 a, c  right triangle sides
Isosceles triangle, through angle and side
 Measure the one angle of the triangle and the opposite side to that angle.

Use the angle and the side values to calculate the bisector using the following formula: l = m = h = asin(\alpha)Where:
 l = m = h  in isosceles triangle bisector median and height are the same
 a  isosceles triangle side
 \alpha  isosceles triangle angle
Why Triangle Bisectors Matter
The bisectors of a triangle are important for a number of reasons. For example:
 They can be used to find the incenter of the triangle, which is the center of the circle that is tangent to all three sides of the triangle.
 They can be used to construct the medians of the triangle, which are lines that connect each vertex of the triangle to the midpoint of the opposite side.
 They are used in a variety of geometric proofs and constructions.
If you need to calculate the bisectors of a triangle, the triangle bisector calculator can help make the process quick and easy.
 Area
 Volume
 Perimeter
 Side
 Height
 Diagonal
 Radius
 Median
 Bisector
 Angle
 Theorems