Question 960102
Find the slope of the line from B to C. 
Then find the perpendicular bisector of that line that goes through B.
Slope of BC:
{{{m=(12-(-3))/(6-3)=15/3=5}}}
Since the lines are perpendicular, their slopes are negative reciprocals,
{{{m[p]*5=-1}}}
{{{m[p]=-1/5}}}
Using the point-slope form,
{{{y-3=-(1/5)(x-(-3))}}}
{{{y-3=-(1/5)(x+3)}}}
{{{y-3=-(1/5)x-3/5}}}
{{{y=-(1/5)x-3/5+15/5}}}
{{{highlight(y=-(1/5)x+12/5)}}}
.
.
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{{{drawing(300,300,-6,10,-4,12,grid(1),
circle(-3,3,0.2),
circle(3,-3,0.2),
circle(6,12,0.2),
blue(line(-3,3,3,-3)),
blue(line(3,-3,6,12)),
blue(line(6,12,-3,3)),
graph(300,300,-6,10,-4,12,-x/5+12/5))}}}