Question

question 1-20
fill in the blanks using the available answer choices.
in $\triangle abc$, $\overline{dg}$ is the perpendicular bisector of $\overline{bc}$ and $\overline{eg}$ is the perpendicular bisector of $\overline{ac}$.
to construct the \boxed{} of $\triangle abc$, draw a circle with center \boxed{} and radius \boxed{}.
image of triangle abc with perpendicular bisectors dg (for bc) and eg (for ac), and intersection point g, plus points d, e, f

Explanation:

Step1: Recall Circumcircle Construction

To construct the circumcircle of a triangle, we use the circumcenter (intersection of perpendicular bisectors) as the center and the distance from circumcenter to any vertex as the radius.

Step2: Identify Perpendicular Bisectors

Given \( DG \) is perpendicular bisector of \( BC \), \( EG \) is perpendicular bisector of \( AC \). Their intersection \( G \) is the circumcenter.

Step3: Determine Radius

Radius is the distance from \( G \) to any vertex (e.g., \( GA \), \( GB \), or \( GC \)).

Step4: Fill the Blanks

1. First blank: "circumcircle" (as we're constructing the circumcircle of \( \triangle ABC \)).
2. Second blank: "G" (the circumcenter, intersection of perpendicular bisectors).
3. Third blank: "GA" (or \( GB \), \( GC \); distance from center \( G \) to vertex \( A \) is radius).

Answer:

1. circumcircle
2. \( G \)
3. \( GA \) (or \( GB \), \( GC \))