Suppose you have a triangle ABC you want to draw the excircle relative to BC.

1. Draw triangle ABC.
2. Draw line $f$ passing through A and B.
3. Draw line $g$ passing through A and C.
4. Plot point D on line f and point E on line g (ensuring they lie past points B and C respectively to extend the sides).
5. Draw the angle bisector for angles CBD and BCE. Let F be the intersection point of those two bisectors. F is the excenter.
6. Draw a perpendicular line to BC that passes through F. Plot intersection point G between this perpendicular line and BC.
7. Draw circle d centered at F that passes through G.