the equations of perpendicular bisectors of the sides AB and AC of a triangle ABC are x-y+5=0 and x+2y=0 respectively.If this point A(1,-2) the equation of the line BC is
Step 1. Find the point, D, where those two lines intersect.
Step 2. Find the distance, d(A,D). The is the circum-radius.
Step 3. Write the equations of the two lines through A each of which is perpendicular to one of the given lines
Step 4. Find the points on the lines in step 3 where the circum-circle insects.
Step 5: Those points are B & C.
1. Since $\displaystyle AC \perp g$ the line AC has the slope $\displaystyle m_{AC} = 2$. Use point-slope-formula to determine the equation of
$\displaystyle AC: y+2=2(x-1)$
2. $\displaystyle AC\ \cap g = M_{AC}$
$\displaystyle 2x-4 = -\frac12 x~\implies~x=\frac85$
Consequently the midpoint of $\displaystyle \overline{AC}$ is $\displaystyle M_{AC}\left(\frac85\ ,\ -\frac45\right)$
Now you can determine the coordinates of point C: $\displaystyle C\left(\frac{11}5\ ,\ \frac25\right)$
3. The same method will give you the point B: $\displaystyle B(-7, 6)$
4. Use the coordinates of B and C to determine the equation of BC.