Question

1. to construct the circumscribed circle of a triangle, you must construct at least two of the

□ altitudes
□ angle bisectors
□ medians
■ perpendicular bisectors
of the triangle and find their intersection point.
set your compass to the distance from the circumcenter to
□ a point where a perpendicular bisector intersects the triangle.
■ a vertex of the triangle.
□ any point.
place the point of the compass on
□ any vertex of the triangle
■ the circumcenter
and draw a circle with the compass.

Explanation:

To construct the circumscribed circle (circumcircle) of a triangle:

1. The circumcenter is the intersection of the perpendicular bisectors of the triangle's sides. So we need to construct at least two perpendicular bisectors (correct option: perpendicular bisectors).
2. The radius of the circumcircle is the distance from the circumcenter to any vertex of the triangle (since all vertices lie on the circle), so we set the compass to the distance from circumcenter to a vertex (correct option: a vertex of the triangle).
3. The compass point is placed on the circumcenter (the center of the circle) to draw the circle (correct option: the circumcenter).

Answer:

• For the first blank (construction lines): perpendicular bisectors (selected in the image, which is correct as circumcenter is where perpendicular bisectors meet).
• For the second blank (compass distance): a vertex of the triangle (selected in the image, correct as radius is circumcenter - vertex distance).
• For the third blank (compass placement): the circumcenter (selected in the image, correct as circumcenter is the center of the circumcircle).