High School How Is the Gradient of an Angle Bisector Determined from Two Intersecting Lines?

[Einstein's Cat]

Say there are two lines that can be described as y=m1x + c1 and y= m2x + c2; they intercept at the point (x, y). There's a line that will bisect the angle that the two lines form as they intercept and it can be described as y= m3x + c3; this line will also intercept the other two lines at (x, y).

What is the relationship between the gradients of the two lines (m1 and m2) and the gradient of the angle bisector (m3)?
Or else, say if you know the values of m1 and c1, m2 and c2; what will be the value of m3 and c3?

 

[BvU]

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