Question

question 3 of 5 drag each tile to the correct box. the steps for constructing a circle circumscribed about triangle pqr are listed out of order. arrange the steps in the correct sequence. a construct a circle centered at o with radius equal to oa, ob, or oc. b label the intersection of the perpendicular bisectors o. c construct the perpendicular bisectors of ab and bc.

Explanation:

Step1: First find the center

Construct the perpendicular bisectors of the sides of the triangle. The intersection of these perpendicular bisectors is the center \(O\) of the circum - circle. So the first step is C. Construct the perpendicular bisectors of \(\overline{AB}\) and \(\overline{BC}\).

Step2: Then determine the radius

Once the center \(O\) is found, the distance from the center \(O\) to any of the vertices of the triangle (e.g., \(OA\), \(OB\), or \(OC\)) is the radius of the circum - circle. So the second step is B. Label the intersection of the perpendicular bisectors \(O\).

Step3: Finally construct the circle

With the center \(O\) and radius equal to \(OA\), \(OB\), or \(OC\), construct the circle. So the third step is A. Construct a circle centered at \(O\) with radius equal to \(OA\), \(OB\), or \(OC\).

Answer:

1. C. Construct the perpendicular bisectors of \(\overline{AB}\) and \(\overline{BC}\).
2. B. Label the intersection of the perpendicular bisectors \(O\).
3. A. Construct a circle centered at \(O\) with radius equal to \(OA\), \(OB\), or \(OC\).