Question

How to find equation of angle bisector in a triangle?

Answer 1

Answer:

Step-by-step explanation:Basically you want to find the equations of the angle bisector of any two lines taken at a time.

Consider the first two lines, l1=3x+4y=6 and l2=12x−5y=3

We know that any point on the angle bisector of two lines is equidistant from the two lines.

Also the perpendicular distance of a point (x1,y1) to a line ax +by + c = 0 is given by:

D = |ax1+by1+c|a2+b2√

From the above two facts, the equation of the angle bisector can be written as:

3x+4y−632+42√=12x−5y−3122+52√

3x+4y−65=±12x−5y−313

You can solve the above to get two different equations, one of which would be of the internal angle bisector and the other of the external.

We can rewrite the two equations as functions below:

f1(x,y)=3x+4y−65+12x−5y−313=0, and

f2(x,y)=3x+4y−65−12x−5y−313=0

Now, let us assume we calculated the above equations for ∠A of △ABC.

To determine which of the above two equations, you first need to find out the points B and C, by solving for lines l1,l3 and l2,l3 and then evaluate,

F=fi(B)∗fi(C) for i = 1, 2

The one with F < 0, is the equation of internal angle bisector.

Similarly, we can find for other angles as well.