Doug C. answered • 06/28/18

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Hi Billy,

It is the 4th choice that is similar for the two constructions.

The 3 angle bisectors of a triangle meet at a common point. After constructing two of them, that point is the center of the inscribed circle. You still have to construct a perpendicular through that point to one of the sides of the triangle. The point where the perpendicular intersects the side of the triangle will help determine the opening of the compass when drawing the inscribed circle. The final step will be to place the compass point on the intersection point of the angle bisectors and draw the circle.

The perpendicular bisectors of each side of a triangle also meet at a common point (which will be the center of the circumscribed circle). After constructing two of the perpendicular bisectors, place the compass point on the point of intersection, open the compass so that the pencil touches one of the vertices of the triangle (this is the radius of the circumscribed circle. The final step will be similar to the 4th choice of your listed choices.

If you are not sure how to construct angle bisectors and/or perpendicular bisectors do a search for something like "construct circle inscribed in triangle".