Question 834288
Since cd is perpendicular to AB we have two right triangles
cad and cbd

Since cd bisects ab then ad =db

we have 
ad^2+cd^2=ca^2
and
db^2+cd^2=cb^2
but since
ad=db then 
ad^2=db^2
therefore 
ad^2+cd^2=db^2+cd^2
hence
ca^2=cb^2

therefore
 ca=cb

QED