Axiomic geometry bisectors

Question

Find the bisector of the angle ABC if A= (0,5), B= (0,3), C= (2, square root of 21)

Answer 1

Here is a picture showing the given points and the resulting triangle ABC. The blue line is the bisector of angle B.

CD=√21-3, so CB̂D=tan^-1(CD/BD)=tan^-1((√21-3)/2)=38.354° approx.

AB̂C=BĈD=90-CB̂D=51.646°, ½AB̂C=25.823°, which is the angle bisector of B.